Theorem pm2.86d 93

Description: Deduction based on pm2.86 94. (Contributed by NM, 29-Jun-1995.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)

Hypothesis

Ref	Expression
pm2.86d.1	|- (ph -> ((ps -> ch) -> (ps -> th)))

Assertion

Ref	Expression
pm2.86d	|- (ph -> (ps -> (ch -> th)))

Proof of Theorem pm2.86d

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 |- (ch -> (ps -> ch))
2		pm2.86d.1	. . 3 |- (ph -> ((ps -> ch) -> (ps -> th)))
3	1, 2	syl5 28	. 2 |- (ph -> (ch -> (ps -> th)))
4	3	com23 72	1 |- (ph -> (ps -> (ch -> th)))

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  pm2.86  94  pm5.74  235  ax12olem6  1932  ax15  2021