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Theorem 3anandis 1279
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 107 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ph )
2 simpr1 945 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ps )
3 simpr2 946 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ch )
4 simpr3 947 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  th )
5 3anandis.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ( ph  /\  ch )  /\  ( ph  /\  th ) )  ->  ta )
61, 2, 1, 3, 1, 4, 5syl222anc 1186 1  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  th )
)  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by: (None)
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