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Theorem rmobii 3322
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 3321 1 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 197  wcel 2156  ∃*wrmo 3099
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001
This theorem depends on definitions:  df-bi 198  df-an 385  df-tru 1641  df-ex 1860  df-eu 2634  df-mo 2635  df-rmo 3104
This theorem is referenced by:  reuxfr2d  5088  brdom7disj  9638  reuxfr3d  29655  cvmlift2lem13  31620  nomaxmo  32168  ineccnvmo  34435  2reu5a  41689
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