Theorem efald 1334

Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.)

Hypothesis

Ref	Expression
efald.1	|- ((ph /\ -. ps) -> F. )

Assertion

Ref	Expression
efald	|- (ph -> ps)

Proof of Theorem efald

Step	Hyp	Ref	Expression
1		efald.1	. . 3 |- ((ph /\ -. ps) -> F. )
2	1	inegd 1333	. 2 |- (ph -> -. -. ps)
3	2	notnotrd 105	1 |- (ph -> ps)

Syntax hints:  -. wn 3   -> wi 4   /\ wa 358   F. wfal 1317

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-fal 1320

This theorem is referenced by: (None)