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Theorem 2rexbii 2641
 Description: Inference adding two restricted existential quantifiers to both sides of an equivalence. (Contributed by NM, 11-Nov-1995.)
Hypothesis
Ref Expression
ralbii.1 (φψ)
Assertion
Ref Expression
2rexbii (x A y B φx A y B ψ)

Proof of Theorem 2rexbii
StepHypRef Expression
1 ralbii.1 . . 3 (φψ)
21rexbii 2639 . 2 (y B φy B ψ)
32rexbii 2639 1 (x A y B φx A y B ψ)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  ∃wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-rex 2620 This theorem is referenced by:  3reeanv  2779  addccom  4406  addcass  4415  ncfinraise  4481  ncfinlower  4483  nnpweq  4523  dfxp2  5113  peano4nc  6150  sbth  6206
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