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Theorem ralcomf 2926
 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:   ,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem ralcomf
StepHypRef Expression
1 ancomst 453 . . . 4
212albii 1686 . . 3
3 alcom 1899 . . 3
42, 3bitri 252 . 2
5 ralcomf.1 . . 3
65r2alf 2741 . 2
7 ralcomf.2 . . 3
87r2alf 2741 . 2
94, 6, 83bitr4i 280 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435   wcel 1872  wnfc 2556  wral 2714 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-ex 1658  df-nf 1662  df-sb 1791  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ral 2719 This theorem is referenced by:  ralcom  2928  ssiinf  4291  ralcom4f  28052
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