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Theorem rmobiia 2493
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 427 . . 3 ((x A φ) ↔ (x A ψ))
32mobii 1934 . 2 (∃*x(x A φ) ↔ ∃*x(x A ψ))
4 df-rmo 2308 . 2 (∃*x A φ∃*x(x A φ))
5 df-rmo 2308 . 2 (∃*x A ψ∃*x(x A ψ))
63, 4, 53bitr4i 201 1 (∃*x A φ∃*x A ψ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98   wcel 1390  ∃*wmo 1898  ∃*wrmo 2303
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-eu 1900  df-mo 1901  df-rmo 2308
This theorem is referenced by:  rmobii  2494
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