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Theorem rmobiia 2801
 Description: Formula-building rule for restricted existential quantifier (inference rule). (Contributed by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmobiia.1 (x A → (φψ))
Assertion
Ref Expression
rmobiia (∃*x A φ∃*x A ψ)

Proof of Theorem rmobiia
StepHypRef Expression
1 rmobiia.1 . . . 4 (x A → (φψ))
21pm5.32i 618 . . 3 ((x A φ) ↔ (x A ψ))
32mobii 2240 . 2 (∃*x(x A φ) ↔ ∃*x(x A ψ))
4 df-rmo 2622 . 2 (∃*x A φ∃*x(x A φ))
5 df-rmo 2622 . 2 (∃*x A ψ∃*x(x A ψ))
63, 4, 53bitr4i 268 1 (∃*x A φ∃*x A ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   ∈ wcel 1710  ∃*wmo 2205  ∃*wrmo 2617 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 2622 This theorem is referenced by:  rmobii  2802
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