Theorem anandirs 595

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 590	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ ch ) ) -> ta )
3	2	anabsan2 584	1 |- ( ( ( ph /\ ps ) /\ ch ) -> ta )

Syntax hints:   -> wi 4   /\ wa 104

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

This theorem is referenced by:  3impdir  1328  fvreseq  5740  phplem4  7024  muladd  8541  iccshftr  10202  iccshftl  10204  iccdil  10206  icccntr  10208  fzaddel  10267  fzsubel  10268  mulexp  10812  upxp  14961  uptx  14963