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Theorem rmobidv 3397
Description: Formula-building rule for restricted at-most-one quantifier (deduction form). (Contributed by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmobidv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
rmobidv (𝜑 → (∃*𝑥𝐴 𝜓 ↔ ∃*𝑥𝐴 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 480 . 2 ((𝜑𝑥𝐴) → (𝜓𝜒))
32rmobidva 3395 1 (𝜑 → (∃*𝑥𝐴 𝜓 ↔ ∃*𝑥𝐴 𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wcel 2108  ∃*wrmo 3379
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-mo 2540  df-rmo 3380
This theorem is referenced by:  rmoeqd  3420  brdom7disj  10571  ddemeas  34237  poimirlem26  37653
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