Theorem anandis 587

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 583	. 2 |- ( ( ( ph /\ ph ) /\ ( ps /\ ch ) ) -> ta )
3	2	anabsan 570	1 |- ( ( ph /\ ( ps /\ ch ) ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  3impdi  1288  dff13  5747  f1oiso  5805  ltapig  7300  ltmpig  7301  faclbnd  10675  tgcl  12858