Users' Mathboxes Mathbox for Rodolfo Medina < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  jca3 Unicode version

Theorem jca3 26813
Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 14-Oct-2010.)
Hypotheses
Ref Expression
jca3.1  |-  ( ph  ->  ( ps  ->  ch ) )
jca3.2  |-  ( th 
->  ta )
Assertion
Ref Expression
jca3  |-  ( ph  ->  ( ps  ->  ( th  ->  ( ch  /\  ta ) ) ) )

Proof of Theorem jca3
StepHypRef Expression
1 jca3.1 . . . . 5  |-  ( ph  ->  ( ps  ->  ch ) )
21imp 418 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
32a1d 22 . . 3  |-  ( (
ph  /\  ps )  ->  ( th  ->  ch ) )
4 jca3.2 . . 3  |-  ( th 
->  ta )
53, 4jca2 26811 . 2  |-  ( (
ph  /\  ps )  ->  ( th  ->  ( ch  /\  ta ) ) )
65ex 423 1  |-  ( ph  ->  ( ps  ->  ( th  ->  ( ch  /\  ta ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
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