Theorem exp4a 358

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 259	. 2 |- ( ( ( ch /\ th ) -> ta ) <-> ( ch -> ( th -> ta ) ) )
3	1, 2	syl6ib 159	1 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  exp4b  359  exp4d  361  exp45  366  exp5c  368  tfri3  5976  nnmordi  6112  ndvdssub  10330