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Theorem 3anandirs 1254
Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 25-Jul-2006.) (Revised by NM, 18-Apr-2007.)
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 918 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ph )
2 simpr 107 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  th )
3 simpl2 919 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ps )
4 simpl3 920 . 2  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ch )
5 3anandirs.1 . 2  |-  ( ( ( ph  /\  th )  /\  ( ps  /\  th )  /\  ( ch 
/\  th ) )  ->  ta )
61, 2, 3, 2, 4, 2, 5syl222anc 1162 1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    /\ w3a 896
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  df-3an 898
This theorem is referenced by: (None)
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