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Theorem rexcom4bOLD 26448
Description: Specialized existential commutation lemma. (Moved to rexcom4b 2822 in main set.mm and may be deleted by mathbox owner, JM. --NM 16-Apr-2012.) (Contributed by Jeff Madsen, 1-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
rexcom4bOLD.1  |-  B  e. 
_V
Assertion
Ref Expression
rexcom4bOLD  |-  ( E. x E. y  e.  A  ( ph  /\  x  =  B )  <->  E. y  e.  A  ph )
Distinct variable groups:    x, A    x, y    ph, x    x, B
Allowed substitution hints:    ph( y)    A( y)    B( y)

Proof of Theorem rexcom4bOLD
StepHypRef Expression
1 rexcom4bOLD.1 . 2  |-  B  e. 
_V
21rexcom4b 2822 1  |-  ( E. x E. y  e.  A  ( ph  /\  x  =  B )  <->  E. y  e.  A  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   E.wex 1531    = wceq 1632    e. wcel 1696   E.wrex 2557   _Vcvv 2801
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-v 2803
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