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Theorem raaanv 3307
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 1402 . 2 yφ
2 nfv 1402 . 2 xψ
31, 2raaan 3306 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 2284
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2289
This theorem is referenced by:  reusv3i  4141  f1mpt  5335
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