Theorem pm2.18da 459

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

Hypothesis

Ref	Expression
pm2.18da.1	|- ( ( ph /\ -. ps ) -> ps )

Assertion

Ref	Expression
pm2.18da	|- ( ph -> ps )

Proof of Theorem pm2.18da

Step	Hyp	Ref	Expression
1		pm2.18da.1	. . 3 |- ( ( ph /\ -. ps ) -> ps )
2	1	ex 450	. 2 |- ( ph -> ( -. ps -> ps ) )
3	2	pm2.18d 124	1 |- ( ph -> ps )

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

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

This theorem is referenced by:  fpwwe2lem13  9464  bpos  25018  2pwp1prm  41503