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Theorem rmobii 3163
Description: Formula-building rule for restricted existential quantifier (inference rule). (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 3162 1 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wcel 2030  ∃*wrmo 2944
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-eu 2502  df-mo 2503  df-rmo 2949
This theorem is referenced by:  reuxfr2d  4921  brdom7disj  9391  reuxfr3d  29456  cvmlift2lem13  31423  nomaxmo  31972  ineccnvmo  34262  2reu5a  41498
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