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Theorem anandis 803
Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)
Hypothesis
Ref Expression
anandis.1  |-  ( ( ( ph  /\  ps )  /\  ( ph  /\  ch ) )  ->  ta )
Assertion
Ref Expression
anandis  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  ta )

Proof of Theorem anandis
StepHypRef Expression
1 anandis.1 . . 3  |-  ( ( ( ph  /\  ps )  /\  ( ph  /\  ch ) )  ->  ta )
21an4s 799 . 2  |-  ( ( ( ph  /\  ph )  /\  ( ps  /\  ch ) )  ->  ta )
32anabsan 786 1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  3impdi  1237  dff13  5870  f1oiso  5935  omord2  6652  fodomacn  7773  ltapi  8617  ltmpi  8618  axpre-ltadd  8879  faclbnd  11396  pwsdiagmhm  14544  tgcl  16813  grpoinvf  21019  ocorth  21984  fh1  22311  fh2  22312  spansncvi  22345  lnopmi  22694  adjlnop  22780  brbtwn2  25092
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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