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Theorem rexcomf 2472
 Description: Commutation of restricted quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
ralcomf.1
ralcomf.2
Assertion
Ref Expression
rexcomf
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem rexcomf
StepHypRef Expression
1 ancom 253 . . . . 5
21anbi1i 431 . . . 4
322exbii 1497 . . 3
4 excom 1554 . . 3
53, 4bitri 173 . 2
6 ralcomf.1 . . 3
76r2exf 2342 . 2
8 ralcomf.2 . . 3
98r2exf 2342 . 2
105, 7, 93bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  wex 1381   wcel 1393  wnfc 2165  wrex 2307 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312 This theorem is referenced by:  rexcom  2474
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