Theorem imp42 351

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

Hypothesis

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

Assertion

Ref	Expression
imp42	|- ( ( ( ph /\ ( ps /\ ch ) ) /\ th ) -> ta )

Proof of Theorem imp42

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	imp32 255	. 2 |- ( ( ph /\ ( ps /\ ch ) ) -> ( th -> ta ) )
3	2	imp 123	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

This theorem is referenced by:  imp55  358  txbas  12427