Theorem 3anandis 1347

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

Hypothesis

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

Assertion

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

Proof of Theorem 3anandis

Step	Hyp	Ref	Expression
1		simpl 109	. 2 |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ph )
2		simpr1 1003	. 2 |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ps )
3		simpr2 1004	. 2 |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ch )
4		simpr3 1005	. 2 |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> th )
5		3anandis.1	. 2 |- ( ( ( ph /\ ps ) /\ ( ph /\ ch ) /\ ( ph /\ th ) ) -> ta )
6	1, 2, 1, 3, 1, 4, 5	syl222anc 1254	1 |- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 978

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 980

This theorem is referenced by: (None)