Theorem anandirs 597

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 592	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ ch ) ) -> ta )
3	2	anabsan2 586	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  1331  fvreseq  5759  phplem4  7084  muladd  8605  iccshftr  10273  iccshftl  10275  iccdil  10277  icccntr  10279  fzaddel  10339  fzsubel  10340  mulexp  10886  upxp  15066  uptx  15068