Theorem anandis 600

Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)

Hypothesis

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

Assertion

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

Proof of Theorem anandis

Step	Hyp	Ref	Expression
1		anandis.1	. . 3 |- ( ( ( ph /\ ps ) /\ ( ph /\ ch ) ) -> ta )
2	1	an4s 596	. 2 |- ( ( ( ph /\ ph ) /\ ( ps /\ ch ) ) -> ta )
3	2	anabsan 581	1 |- ( ( ph /\ ( ps /\ ch ) ) -> ta )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  3impdi  1334  dff13  5974  f1oiso  6032  ltapig  7705  ltmpig  7706  faclbnd  11179  tgcl  15165