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Theorem anandis 534
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 530 . 2  |-  ( ( ( ph  /\  ph )  /\  ( ps  /\  ch ) )  ->  ta )
32anabsan 517 1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  3impdi  1201  dff13  5435  f1oiso  5493  ltapig  6494  ltmpig  6495  faclbnd  9609
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