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Theorem rmoimi 39732
Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
rmoimi.1 (𝜑𝜓)
Assertion
Ref Expression
rmoimi (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑)

Proof of Theorem rmoimi
StepHypRef Expression
1 rmoimi.1 . . 3 (𝜑𝜓)
21a1i 11 . 2 (𝑥𝐴 → (𝜑𝜓))
32rmoimia 3279 1 (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1938  ∃*wrmo 2803
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-6 1838  ax-7 1885  ax-10 1966  ax-12 1983
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695  df-nf 1699  df-eu 2366  df-mo 2367  df-ral 2805  df-rmo 2808
This theorem is referenced by:  2rexreu  39741
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