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Theorem rmobidv 2800
 Description: Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmobidv.1 (φ → (ψχ))
Assertion
Ref Expression
rmobidv (φ → (∃*x A ψ∃*x A χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem rmobidv
StepHypRef Expression
1 rmobidv.1 . . 3 (φ → (ψχ))
21adantr 451 . 2 ((φ x A) → (ψχ))
32rmobidva 2799 1 (φ → (∃*x A ψ∃*x A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∈ wcel 1710  ∃*wrmo 2617 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-ex 1542  df-nf 1545  df-eu 2208  df-mo 2209  df-rmo 2622 This theorem is referenced by:  rmoeqd  2818
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