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Theorem 3an1rs 1153
Description: Swap conjuncts. (Contributed by NM, 16-Dec-2007.)
Hypothesis
Ref Expression
3an1rs.1  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
Assertion
Ref Expression
3an1rs  |-  ( ( ( ph  /\  ps  /\ 
th )  /\  ch )  ->  ta )

Proof of Theorem 3an1rs
StepHypRef Expression
1 3an1rs.1 . . . . . 6  |-  ( ( ( ph  /\  ps  /\ 
ch )  /\  th )  ->  ta )
21ex 113 . . . . 5  |-  ( (
ph  /\  ps  /\  ch )  ->  ( th  ->  ta ) )
323exp 1140 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
43com34 82 . . 3  |-  ( ph  ->  ( ps  ->  ( th  ->  ( ch  ->  ta ) ) ) )
543imp 1135 . 2  |-  ( (
ph  /\  ps  /\  th )  ->  ( ch  ->  ta ) )
65imp 122 1  |-  ( ( ( ph  /\  ps  /\ 
th )  /\  ch )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 922
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 924
This theorem is referenced by: (None)
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