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Theorem ralcomf 2769
 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 1369 . . . 4
212albii 1567 . . 3
3 alcom 1737 . . 3
42, 3bitri 240 . 2
5 ralcomf.1 . . 3
65r2alf 2649 . 2
7 ralcomf.2 . . 3
87r2alf 2649 . 2
94, 6, 83bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540   wcel 1710  wnfc 2476  wral 2614 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619 This theorem is referenced by:  ralcom  2771  ssiinf  4015
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