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  5806  phplem4  7150  muladd  8705  iccshftr  10379  iccshftl  10381  iccdil  10383  icccntr  10385  fzaddel  10448  fzsubel  10449  mulexp  10998  upxp  15356  uptx  15358