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Theorem r2ex 2652
 Description: Double restricted existential quantification. (Contributed by NM, 11-Nov-1995.)
Assertion
Ref Expression
r2ex (x A y B φxy((x A y B) φ))
Distinct variable groups:   x,y   y,A
Allowed substitution hints:   φ(x,y)   A(x)   B(x,y)

Proof of Theorem r2ex
StepHypRef Expression
1 nfcv 2489 . 2 yA
21r2exf 2650 1 (x A y B φxy((x A y B) φ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358  ∃wex 1541   ∈ wcel 1710  ∃wrex 2615 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-rex 2620 This theorem is referenced by:  reean  2777  elxpk2  4197  evenfinex  4503  oddfinex  4504  rnoprab2  5577  rnmpt2  5717  lecex  6115  mucnc  6131
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