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Theorem ralcomf 2516
 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 1370 . . . 4
212albii 1401 . . 3
3 alcom 1408 . . 3
42, 3bitri 182 . 2
5 ralcomf.1 . . 3
65r2alf 2384 . 2
7 ralcomf.2 . . 3
87r2alf 2384 . 2
94, 6, 83bitr4i 210 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283   wcel 1434  wnfc 2207  wral 2349 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354 This theorem is referenced by:  ralcom  2518  ssiinf  3735
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