Suppose $P$ is a proposition whose truth or falsehood is to be determined.
Let $\phi$ be a WFF of $\mathcal L$.
The term formal proof is also used to refer to specific presentations of such collections.
Also known as
Some authors use the term sound argument as a synonym for what is defined here as a proof.
However, as some use sound argument to mean the same thing that is defined here as a valid argument, it is recommended that this term not be used.
Some authors refer to a proof as a derivation.
- 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S 1.1$: Constants and variables
- 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): $\S 1.2$: Conditionals and Negation
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.1$: The need for logic
- 1995: Merrilee H. Salmon: Introduction to Logic and Critical Thinking: $\S 3.1$
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $1$: Elementary, my dear Watson: $\S 1.1$: You have a logical mind if...: Definition $1.1.3$
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $2$: The Logic of Shape: Euclid
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: proof