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Theorem r19.23v 2539
 Description: Theorem 19.23 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 31-Aug-1999.)
Assertion
Ref Expression
r19.23v (∀𝑥𝐴 (𝜑𝜓) ↔ (∃𝑥𝐴 𝜑𝜓))
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝐴(𝑥)

Proof of Theorem r19.23v
StepHypRef Expression
1 nfv 1508 . 2 𝑥𝜓
21r19.23 2538 1 (∀𝑥𝐴 (𝜑𝜓) ↔ (∃𝑥𝐴 𝜑𝜓))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104  ∀wral 2414  ∃wrex 2415 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  ax-i5r 1515 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-ral 2419  df-rex 2420 This theorem is referenced by:  uniiunlem  3180  dfiin2g  3841  iunss  3849  ralxfr2d  4380  rexxfr2d  4381  ssrel2  4624  reliun  4655  funimaexglem  5201  funimass4  5465  ralrnmpo  5878
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