True Statement is implied by Every Statement
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Theorem
If something is true, then anything implies it.
Formulation 1
\(\ds p\) | \(\) | \(\ds \) | ||||||||||||
\(\ds \vdash \ \ \) | \(\ds q \implies p\) | \(\) | \(\ds \) |
Formulation 2
- $\vdash q \implies \paren {p \implies q}$
Also see
- Paradoxes of Material Implication, in which category this result is grouped
Sources
- 1959: A.H. Basson and D.J. O'Connor: Introduction to Symbolic Logic (3rd ed.) ... (previous) ... (next): $\S 2.3$: Basic Truth-Tables of the Propositional Calculus