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Theorem bnj1265 29184
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1265.1  |-  ( ph  ->  E. x  e.  A  ps )
Assertion
Ref Expression
bnj1265  |-  ( ph  ->  ps )
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x)    A( x)

Proof of Theorem bnj1265
StepHypRef Expression
1 bnj1265.1 . . . 4  |-  ( ph  ->  E. x  e.  A  ps )
21bnj1196 29166 . . 3  |-  ( ph  ->  E. x ( x  e.  A  /\  ps ) )
32bnj1266 29183 . 2  |-  ( ph  ->  E. x ps )
43bnj937 29142 1  |-  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   E.wrex 2706
This theorem is referenced by:  bnj1253  29386  bnj1280  29389  bnj1296  29390  bnj1371  29398  bnj1497  29429
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-rex 2711
  Copyright terms: Public domain W3C validator