Theorem imp4a 347

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 261	. 2 |- ( ( ( ch /\ th ) -> ta ) <-> ( ch -> ( th -> ta ) ) )
3	1, 2	syl6ibr 161	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:  imp4b  348  imp4d  350  imp55  359  imp511  360  equs5or  1818  reuss2  3402  tfrlem9  6287  facwordi  10653  ndvdssub  11867  neibl  13131