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Theorem ralcomf 3016
 Description: Commutation of restricted universal quantifiers. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
ralcomf.1
ralcomf.2
Assertion
Ref Expression
ralcomf
Distinct variable group:   ,

Proof of Theorem ralcomf
StepHypRef Expression
1 ancomst 452 . . . 4
212albii 1641 . . 3
3 alcom 1845 . . 3
42, 3bitri 249 . 2
5 ralcomf.1 . . 3
65r2alf 2833 . 2
7 ralcomf.2 . . 3
87r2alf 2833 . 2
94, 6, 83bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  e.wcel 1818  F/_wnfc 2605  A.wral 2807 This theorem is referenced by:  ralcom  3018  ssiinf  4379  ralcom4f  27375 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812
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