Theorem imp4a 349

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 263	. 2 |- ( ( ( ch /\ th ) -> ta ) <-> ( ch -> ( th -> ta ) ) )
3	1, 2	imbitrrdi 162	1 |- ( ph -> ( ps -> ( ( ch /\ th ) -> ta ) ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  imp4b  350  imp4d  352  imp55  361  imp511  362  equs5or  1844  reuss2  3444  tfrlem9  6386  facwordi  10849  ndvdssub  12112  neibl  14811