Theorem imp43 347

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

Hypothesis

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

Assertion

Ref	Expression
imp43	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ta )

Proof of Theorem imp43

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	imp4b 342	. 2 |- ( ( ph /\ ps ) -> ( ( ch /\ th ) -> ta ) )
3	2	imp 122	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:  fundmen  6309  divgt0  7950  divge0  7951  le2sq2  9551