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Theorem jca2r 26812
Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 17-Oct-2010.)
Hypotheses
Ref Expression
jca2r.1  |-  ( ph  ->  ( ps  ->  ch ) )
jca2r.2  |-  ( ps 
->  th )
Assertion
Ref Expression
jca2r  |-  ( ph  ->  ( ps  ->  ( th  /\  ch ) ) )

Proof of Theorem jca2r
StepHypRef Expression
1 jca2r.2 . . 3  |-  ( ps 
->  th )
21a1i 10 . 2  |-  ( ph  ->  ( ps  ->  th )
)
3 jca2r.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3jcad 519 1  |-  ( ph  ->  ( ps  ->  ( th  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  prter2  26852
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator