Theorem exp4a 363

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  364  exp4d  366  exp45  371  exp5c  373  tfri3  6257  nnmordi  6405  fiintim  6810  ndvdssub  11616  iscnp4  12376  metcnp3  12669