Theorem imim12d 68

Description: Deduction combining antecedents and consequents. (Contributed by NM, 7-Aug-1994.) (Proof shortened by O'Cat, 30-Oct-2011.)

Hypotheses

Ref	Expression
imim12d.1	|- (ph -> (ps -> ch))
imim12d.2	|- (ph -> (th -> ta))

Assertion

Ref	Expression
imim12d	|- (ph -> ((ch -> th) -> (ps -> ta)))

Proof of Theorem imim12d

Step	Hyp	Ref	Expression
1		imim12d.1	. 2 |- (ph -> (ps -> ch))
2		imim12d.2	. . 3 |- (ph -> (th -> ta))
3	2	imim2d 48	. 2 |- (ph -> ((ch -> th) -> (ch -> ta)))
4	1, 3	syl5d 62	1 |- (ph -> ((ch -> th) -> (ps -> ta)))

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:  imim1d  69  equveli  1988  mo  2226  rspcimdv  2957