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Theorem anandirs 558
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
StepHypRef Expression
1 anandirs.1 . . 3  |-  ( ( ( ph  /\  ch )  /\  ( ps  /\  ch ) )  ->  ta )
21an4s 553 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  ->  ta )
32anabsan2 549 1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  3impdir  1226  fvreseq  5303  phplem4  6390  muladd  7555  iccshftr  9092  iccshftl  9094  iccdil  9096  icccntr  9098  fzaddel  9153  fzsubel  9154  mulexp  9612
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