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Theorem bnj240 28724
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 976 . . 3  |-  ( ( ps  /\  ch  /\  ph )  ->  ps' )
3 bnj240.2 . . . 4  |-  ( ch 
->  ch' )
433ad2ant2 977 . . 3  |-  ( ( ps  /\  ch  /\  ph )  ->  ch' )
52, 4jca 518 . 2  |-  ( ( ps  /\  ch  /\  ph )  ->  ( ps'  /\  ch' ) )
653comr 1159 1  |-  ( (
ph  /\  ps  /\  ch )  ->  ( ps'  /\  ch' ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  bnj594  28944  bnj580  28945  bnj966  28976  bnj967  28977
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  df-3an 936
  Copyright terms: Public domain W3C validator