Theorem 3anandirs 1279

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 941	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ph )
2		simpr 108	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> th )
3		simpl2 942	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ps )
4		simpl3 943	. 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 1185	1 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 919

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 921

This theorem is referenced by: (None)