Theorem imp43 353

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 348	. 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  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  fundmen  6784  fiintim  6906  divgt0  8788  divge0  8789  le2sq2  10551  basis2  12840  dvidlemap  13454