Theorem exp4a 364

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 261	. 2 |- ( ( ( ch /\ th ) -> ta ) <-> ( ch -> ( th -> ta ) ) )
3	1, 2	syl6ib 160	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  exp4b  365  exp4d  367  exp45  372  exp5c  374  tfri3  6346  nnmordi  6495  fiintim  6906  ndvdssub  11889  iscnp4  13012  metcnp3  13305