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Theorem ralcom 2771
 Description: Commutation of restricted quantifiers. (Contributed by NM, 13-Oct-1999.) (Revised by Mario Carneiro, 14-Oct-2016.)
Assertion
Ref Expression
ralcom (x A y B φy B x A φ)
Distinct variable groups:   x,y   x,B   y,A
Allowed substitution hints:   φ(x,y)   A(x)   B(y)

Proof of Theorem ralcom
StepHypRef Expression
1 nfcv 2489 . 2 yA
2 nfcv 2489 . 2 xB
31, 2ralcomf 2769 1 (x A y B φy B x A φ)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  ∀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:  ralcom4  2877  ssint  3942  iinrab2  4029  fununi  5160  isocnv2  5492
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