Theorem anandirs 601

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 596	. 2 |- ( ( ( ph /\ ps ) /\ ( ch /\ ch ) ) -> ta )
3	2	anabsan2 590	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:  3impdir  1335  fvreseq  5812  phplem4  7156  muladd  8711  iccshftr  10396  iccshftl  10398  iccdil  10400  icccntr  10402  fzaddel  10465  fzsubel  10466  mulexp  11015  upxp  15373  uptx  15375