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Theorem anandirs 582
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 577 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  ch ) )  ->  ta )
32anabsan2 573 1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  3impdir  1272  fvreseq  5524  phplem4  6749  muladd  8158  iccshftr  9789  iccshftl  9791  iccdil  9793  icccntr  9795  fzaddel  9851  fzsubel  9852  mulexp  10344  upxp  12455  uptx  12457
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