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Theorem rmobii 2474
Description: Formula-building rule for restricted existential quantifier (inference rule). (Contributed by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmobii.1 (φψ)
Assertion
Ref Expression
rmobii (∃*x A φ∃*x A ψ)

Proof of Theorem rmobii
StepHypRef Expression
1 rmobii.1 . . 3 (φψ)
21a1i 9 . 2 (x A → (φψ))
32rmobiia 2473 1 (∃*x A φ∃*x A ψ)
Colors of variables: wff set class
Syntax hints:  wb 98   wcel 1370  ∃*wrmo 2283
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 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377  ax-17 1396  ax-ial 1405
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-eu 1881  df-mo 1882  df-rmo 2288
This theorem is referenced by: (None)
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