Theorem 3anandirs 1359

Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.) (Revised by NM, 18-Apr-2007.)

Hypothesis

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

Assertion

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

Proof of Theorem 3anandirs

Step	Hyp	Ref	Expression
1		simpl1 1002	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ph )
2		simpr 110	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> th )
3		simpl2 1003	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ps )
4		simpl3 1004	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ch )
5		3anandirs.1	. 2 |- ( ( ( ph /\ th ) /\ ( ps /\ th ) /\ ( ch /\ th ) ) -> ta )
6	1, 2, 3, 2, 4, 2, 5	syl222anc 1265	1 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by: (None)