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Theorem rmobii 3308
Description: Formula-building rule for restricted existential quantifier (inference form). (Contributed by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmobii.1 (𝜑𝜓)
Assertion
Ref Expression
rmobii (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥𝐴 𝜓)

Proof of Theorem rmobii
StepHypRef Expression
1 rmobii.1 . . 3 (𝜑𝜓)
21a1i 11 . 2 (𝑥𝐴 → (𝜑𝜓))
32rmobiia 3307 1 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wcel 2110  ∃*wrmo 3064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788  df-mo 2539  df-rmo 3069
This theorem is referenced by:  2reu5a  3657  reuxfrd  3661  brdom7disj  10145  2sqreulem4  26335  reuxfrdf  30558  cvmlift2lem13  32990  nomaxmo  33638  ineccnvmo  36226  dfeldisj5  36569  lubeldm2  45923  glbeldm2  45924
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