Theorem 3impib 1137

Description: Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

Hypothesis

Ref	Expression
3impib.1	|- ( ph -> ( ( ps /\ ch ) -> th ) )

Assertion

Ref	Expression
3impib	|- ( ( ph /\ ps /\ ch ) -> th )

Proof of Theorem 3impib

Step	Hyp	Ref	Expression
1		3impib.1	. . 3 |- ( ph -> ( ( ps /\ ch ) -> th ) )
2	1	expd 254	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	3imp 1133	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 920

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  df-3an 922

This theorem is referenced by:  mob  2784  eqreu  2794  funimaexglem  5034  ssimaexg  5288  dfsmo2  5957  3ecoptocl  6283  distrnq0  6747  addassnq0  6750  uzind  8575  fzind  8579  fnn0ind  8580  xltnegi  9014  facwordi  9800  shftvalg  9909  shftval4g  9910  mulgcd  10596  coprmdvds1  10664  speano5  10990