Theorem a1i13 24

Description: Add two antecedents to a wff. (Contributed by Jeff Hankins, 4-Aug-2009.)

Hypothesis

Ref	Expression
a1i13.1	|- ( ps -> th )

Assertion

Ref	Expression
a1i13	|- ( ph -> ( ps -> ( ch -> th ) ) )

Proof of Theorem a1i13

Step	Hyp	Ref	Expression
1		a1i13.1	. . 3 |- ( ps -> th )
2	1	a1d 22	. 2 |- ( ps -> ( ch -> th ) )
3	2	a1i 9	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:  xpfi  7239  seq3fveq2  10912  seq3shft2  10918  seqshft2g  10919  seq3split  10925  seqsplitg  10926