Theorem exp4a 366

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp4a.1	|- ( ph -> ( ps -> ( ( ch /\ th ) -> ta ) ) )

Assertion

Ref	Expression
exp4a	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof of Theorem exp4a

Step	Hyp	Ref	Expression
1		exp4a.1	. 2 |- ( ph -> ( ps -> ( ( ch /\ th ) -> ta ) ) )
2		impexp 263	. 2 |- ( ( ( ch /\ th ) -> ta ) <-> ( ch -> ( th -> ta ) ) )
3	1, 2	imbitrdi 161	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  exp4b  367  exp4d  369  exp45  374  exp5c  376  tfri3  6425  nnmordi  6574  fiintim  6992  ndvdssub  12095  iscnp4  14454  metcnp3  14747