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Theorem bnj31 32727
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 2925 . 2  |-  ( E. x  e.  A  ps  ->  E. x  e.  A  ch )
41, 3syl 16 1  |-  ( ph  ->  E. x  e.  A  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wrex 2808
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-ral 2812  df-rex 2813
This theorem is referenced by:  bnj168  32740  bnj110  32870  bnj906  32942  bnj1253  33027  bnj1280  33030  bnj1296  33031  bnj1371  33039  bnj1497  33070  bnj1498  33071  bnj1501  33077
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