MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  rmobii Structured version   Visualization version   GIF version

Theorem rmobii 3359
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 3357 1 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 205  wcel 2106  ∃*wrmo 3350
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 206  df-an 397  df-ex 1782  df-mo 2533  df-rmo 3351
This theorem is referenced by:  2reu5a  3705  reuxfrd  3709  brdom7disj  10476  2sqreulem4  26839  nomaxmo  27083  reuxfrdf  31483  cvmlift2lem13  33996  ineccnvmo  36891  dfeldisj5  37256  lubeldm2  47109  glbeldm2  47110
  Copyright terms: Public domain W3C validator