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Theorem rexcom4b 2979
 Description: Specialized existential commutation lemma. (Contributed by Jeff Madsen, 1-Jun-2011.)
Hypothesis
Ref Expression
rexcom4b.1
Assertion
Ref Expression
rexcom4b
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem rexcom4b
StepHypRef Expression
1 rexcom4a 2978 . 2
2 rexcom4b.1 . . . . 5
32isseti 2964 . . . 4
43biantru 493 . . 3
54rexbii 2732 . 2
61, 5bitr4i 245 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551   wceq 1653   wcel 1726  wrex 2708  cvv 2958 This theorem is referenced by:  islshpat  29889 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-v 2960
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