Theorem efald 1504

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 1503	. 2 |- ( ph -> -. -. ps )
3	2	notnotrd 128	1 |- ( ph -> ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 384   F. wfal 1488

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 197  df-an 386  df-tru 1486  df-fal 1489

This theorem is referenced by:  efald2  33877