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Theorem raaanv 3322
Description: Rearrange restricted quantifiers. (Contributed by NM, 11-Mar-1997.)
Assertion
Ref Expression
raaanv (x A y A (φ ψ) ↔ (x A φ y A ψ))
Distinct variable groups:   φ,y   ψ,x   x,y,A
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem raaanv
StepHypRef Expression
1 nfv 1418 . 2 yφ
2 nfv 1418 . 2 xψ
31, 2raaan 3321 1 (x A y A (φ ψ) ↔ (x A φ y A ψ))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305
This theorem is referenced by:  reusv3i  4157  f1mpt  5353
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