Theorem imp4a 331

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

Hypothesis

Ref	Expression
imp4.1	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Assertion

Ref	Expression
imp4a	|- ( ph -> ( ps -> ( ( ch /\ th ) -> ta ) ) )

Proof of Theorem imp4a

Step	Hyp	Ref	Expression
1		imp4.1	. 2 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2		impexp 250	. 2 |- ( ( ( ch /\ th ) -> ta ) <-> ( ch -> ( th -> ta ) ) )
3	1, 2	syl6ibr 151	1 |- ( ph -> ( ps -> ( ( ch /\ th ) -> ta ) ) )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  imp4b  332  imp4d  334  imp55  343  imp511  344  equs5or  1711  reuss2  3217  tfrlem9  5935