Theorem 3impib 1102

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 245	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	3imp 1098	1 |- ( ( ph /\ ps /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  mob  2723  eqreu  2733  funimaexglem  4982  ssimaexg  5235  dfsmo2  5902  3ecoptocl  6195  distrnq0  6557  addassnq0  6560  uzind  8349  fzind  8353  fnn0ind  8354  xltnegi  8748  shftvalg  9437  shftval4g  9438  speano5  10069