Theorem rmobii 2803

Description: Formula-building rule for restricted existential quantifier (inference rule). (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 10	. 2 ⊢ (x ∈ A → (φ ↔ ψ))
3	2	rmobiia 2802	1 ⊢ (∃*x ∈ A φ ↔ ∃*x ∈ A ψ)

Syntax hints:   ↔ wb 176   ∈ wcel 1710  ∃*wrmo 2618

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208  df-mo 2209  df-rmo 2623

This theorem is referenced by: (None)