Theorem pm2.18d 103

Description: Deduction based on reductio ad absurdum. (Contributed by FL, 12-Jul-2009.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypothesis

Ref	Expression
pm2.18d.1	|- (ph -> (-. ps -> ps))

Assertion

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

Proof of Theorem pm2.18d

Step	Hyp	Ref	Expression
1		pm2.18d.1	. 2 |- (ph -> (-. ps -> ps))
2		pm2.18 102	. 2 |- ((-. ps -> ps) -> ps)
3	1, 2	syl 15	1 |- (ph -> ps)

Syntax hints:  -. wn 3   -> wi 4

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

This theorem is referenced by:  notnot2  104  pm2.61d  150  pm2.18da  430  oplem1  930  ax10lem4  1941  phi11lem1  4595  0cnelphi  4597