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Theorem rmobii 3349
 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 3348 1 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥𝐴 𝜓)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209   ∈ wcel 2111  ∃*wrmo 3109 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-mo 2598  df-rmo 3114 This theorem is referenced by:  2reu5a  3683  reuxfrd  3687  brdom7disj  9944  2sqreulem4  26045  reuxfrdf  30269  cvmlift2lem13  32687  nomaxmo  33326  ineccnvmo  35787  dfeldisj5  36130
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