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Theorem 2rexbii 2444
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 (∃𝑥𝐴𝑦𝐵 𝜑 ↔ ∃𝑥𝐴𝑦𝐵 𝜓)

Proof of Theorem 2rexbii
StepHypRef Expression
1 ralbii.1 . . 3 (𝜑𝜓)
21rexbii 2442 . 2 (∃𝑦𝐵 𝜑 ↔ ∃𝑦𝐵 𝜓)
32rexbii 2442 1 (∃𝑥𝐴𝑦𝐵 𝜑 ↔ ∃𝑥𝐴𝑦𝐵 𝜓)
Colors of variables: wff set class
Syntax hints:  wb 104  wrex 2417
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-rex 2422
This theorem is referenced by:  3reeanv  2601  4fvwrd4  9941  prodmodc  11371
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