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Theorem bnj240 29136
Description:  /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj240.1  |-  ( ps 
->  ps' )
bnj240.2  |-  ( ch 
->  ch' )
Assertion
Ref Expression
bnj240  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ps'  /\  ch' ) )

Proof of Theorem bnj240
StepHypRef Expression
1 bnj240.1 . . . 4  |-  ( ps 
->  ps' )
213ad2ant1 979 . . 3  |-  ( ( ps  /\  ch  /\  ph )  ->  ps' )
3 bnj240.2 . . . 4  |-  ( ch 
->  ch' )
433ad2ant2 980 . . 3  |-  ( ( ps  /\  ch  /\  ph )  ->  ch' )
52, 4jca 520 . 2  |-  ( ( ps  /\  ch  /\  ph )  ->  ( ps'  /\  ch' ) )
653comr 1162 1  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ps'  /\  ch' ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937
This theorem is referenced by:  bnj594  29356  bnj580  29357  bnj966  29388  bnj967  29389
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939
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