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Theorem rmobidvaOLD 3399
Description: Obsolete version of rmobidv 3388 as of 23-Nov-2024. (Contributed by NM, 16-Jun-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
rmobidvaOLD.1 ((𝜑𝑥𝐴) → (𝜓𝜒))
Assertion
Ref Expression
rmobidvaOLD (𝜑 → (∃*𝑥𝐴 𝜓 ↔ ∃*𝑥𝐴 𝜒))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem rmobidvaOLD
StepHypRef Expression
1 nfv 1917 . 2 𝑥𝜑
2 rmobidvaOLD.1 . 2 ((𝜑𝑥𝐴) → (𝜓𝜒))
31, 2rmobida 3397 1 (𝜑 → (∃*𝑥𝐴 𝜓 ↔ ∃*𝑥𝐴 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 396  wcel 2106  ∃*wrmo 3370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1782  df-nf 1786  df-mo 2533  df-rmo 3371
This theorem is referenced by: (None)
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