Modus Ponendo Ponens/Sequent Form/Proof 1

From ProofWiki
Jump to navigation Jump to search

Theorem

$p \implies q, p \vdash q$


Proof

By the tableau method of natural deduction:

$p \implies q, p \vdash q$
Line Pool Formula Rule Depends upon Notes
1 1 $p \implies q$ Premise (None)
2 2 $p$ Premise (None)
3 1, 2 $q$ Modus Ponendo Ponens: $\implies \mathcal E$ 1, 2

$\blacksquare$


Sources