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Theorem bnj31 28745
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj31.1  |-  ( ph  ->  E. x  e.  A  ps )
bnj31.2  |-  ( ps 
->  ch )
Assertion
Ref Expression
bnj31  |-  ( ph  ->  E. x  e.  A  ch )

Proof of Theorem bnj31
StepHypRef Expression
1 bnj31.1 . 2  |-  ( ph  ->  E. x  e.  A  ps )
2 bnj31.2 . . 3  |-  ( ps 
->  ch )
32reximi 2650 . 2  |-  ( E. x  e.  A  ps  ->  E. x  e.  A  ch )
41, 3syl 15 1  |-  ( ph  ->  E. x  e.  A  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wrex 2544
This theorem is referenced by:  bnj168  28758  bnj110  28890  bnj906  28962  bnj1253  29047  bnj1280  29050  bnj1296  29051  bnj1371  29059  bnj1497  29090  bnj1498  29091  bnj1501  29097
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-ral 2548  df-rex 2549
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