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Theorem 3jcad 1162
Description: Deduction conjoining the consequents of three implications. (Contributed by NM, 25-Sep-2005.)
Hypotheses
Ref Expression
3jcad.1  |-  ( ph  ->  ( ps  ->  ch ) )
3jcad.2  |-  ( ph  ->  ( ps  ->  th )
)
3jcad.3  |-  ( ph  ->  ( ps  ->  ta ) )
Assertion
Ref Expression
3jcad  |-  ( ph  ->  ( ps  ->  ( ch  /\  th  /\  ta ) ) )

Proof of Theorem 3jcad
StepHypRef Expression
1 3jcad.1 . . . 4  |-  ( ph  ->  ( ps  ->  ch ) )
21imp 123 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
3 3jcad.2 . . . 4  |-  ( ph  ->  ( ps  ->  th )
)
43imp 123 . . 3  |-  ( (
ph  /\  ps )  ->  th )
5 3jcad.3 . . . 4  |-  ( ph  ->  ( ps  ->  ta ) )
65imp 123 . . 3  |-  ( (
ph  /\  ps )  ->  ta )
72, 4, 63jca 1161 . 2  |-  ( (
ph  /\  ps )  ->  ( ch  /\  th  /\  ta ) )
87ex 114 1  |-  ( ph  ->  ( ps  ->  ( ch  /\  th  /\  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  ixxssixx  9699  iccid  9722  fzen  9837
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