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Theorem ralcomf 2868
 Description: Commutation of restricted quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
ralcomf.1
ralcomf.2
Assertion
Ref Expression
ralcomf
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem ralcomf
StepHypRef Expression
1 ancomsimp 1379 . . . 4
212albii 1577 . . 3
3 alcom 1753 . . 3
42, 3bitri 242 . 2
5 ralcomf.1 . . 3
65r2alf 2742 . 2
7 ralcomf.2 . . 3
87r2alf 2742 . 2
94, 6, 83bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wcel 1726  wnfc 2561  wral 2707 This theorem is referenced by:  ralcom  2870  ssiinf  4142  ralcom4f  23970 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-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712
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