Theorem anandirs 527

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

Hypothesis

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

Assertion

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

Proof of Theorem anandirs

Step	Hyp	Ref	Expression
1		anandirs.1	. . 3 |- ( ( ( ph /\ ch ) /\ ( ps /\ ch ) ) -> ta )
2	1	an4s 522	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ ch ) ) -> ta )
3	2	anabsan2 518	1 |- ( ( ( ph /\ ps ) /\ ch ) -> ta )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  3impdir  1191  fvreseq  5271  phplem4  6318  muladd  7381  iccshftr  8862  iccshftl  8864  iccdil  8866  icccntr  8868  fzaddel  8922  fzsubel  8923  mulexp  9294