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Theorem 3anandirs 1284
Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.)
Hypothesis
Ref Expression
3anandirs.1  |-  ( ( ( ph  /\  th )  /\  ( ps  /\  th )  /\  ( ch 
/\  th ) )  ->  ta )
Assertion
Ref Expression
3anandirs  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )

Proof of Theorem 3anandirs
StepHypRef Expression
1 simpl1 958 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ph )
2 simpr 447 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  th )
3 simpl2 959 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ps )
4 simpl3 960 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ch )
5 3anandirs.1 . 2  |-  ( ( ( ph  /\  th )  /\  ( ps  /\  th )  /\  ( ch 
/\  th ) )  ->  ta )
61, 2, 3, 2, 4, 2, 5syl222anc 1198 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  leoptr  22733
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  df-3an 936
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