Theorem rmobii 3322

Description: Formula-building rule for restricted existential quantifier (inference form). (Contributed by NM, 16-Jun-2017.)

Hypothesis

Ref	Expression
rmobii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
rmobii	⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥 ∈ 𝐴 𝜓)

Proof of Theorem rmobii

Step	Hyp	Ref	Expression
1		rmobii.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
2	1	a1i 11	. 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 ↔ 𝜓))
3	2	rmobiia 3321	1 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥 ∈ 𝐴 𝜓)

Syntax hints:   ↔ wb 205   ∈ wcel 2108  ∃*wrmo 3066

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1784  df-mo 2540  df-rmo 3071

This theorem is referenced by:  2reu5a  3674  reuxfrd  3678  brdom7disj  10218  2sqreulem4  26507  reuxfrdf  30740  cvmlift2lem13  33177  nomaxmo  33828  ineccnvmo  36416  dfeldisj5  36759  lubeldm2  46138  glbeldm2  46139