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Theorem 3anandis 1347
Description: Inference that undistributes a triple conjunction in the antecedent. (Contributed by NM, 18-Apr-2007.)
Hypothesis
Ref Expression
3anandis.1  |-  ( ( ( ph  /\  ps )  /\  ( ph  /\  ch )  /\  ( ph  /\  th ) )  ->  ta )
Assertion
Ref Expression
3anandis  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )

Proof of Theorem 3anandis
StepHypRef Expression
1 simpl 109 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ph )
2 simpr1 1003 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ps )
3 simpr2 1004 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ch )
4 simpr3 1005 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  th )
5 3anandis.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ph  /\  ch )  /\  ( ph  /\  th ) )  ->  ta )
61, 2, 1, 3, 1, 4, 5syl222anc 1254 1  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by: (None)
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