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Theorem rexcom 2595
 Description: Commutation of restricted quantifiers. (Contributed by NM, 19-Nov-1995.) (Revised by Mario Carneiro, 14-Oct-2016.)
Assertion
Ref Expression
rexcom
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem rexcom
StepHypRef Expression
1 nfcv 2281 . 2
2 nfcv 2281 . 2
31, 2rexcomf 2593 1
 Colors of variables: wff set class Syntax hints:   wb 104  wrex 2417 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422 This theorem is referenced by:  rexcom13  2596  rexcom4  2709  iuncom  3819  xpiundi  4597  addcomprg  7393  mulcomprg  7395  ltexprlemm  7415  caucvgprprlemexbt  7521  suplocexprlemml  7531  suplocexprlemmu  7533  qmulz  9422  caubnd2  10896  sqrt2irr  11847
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