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Theorem rmoimia 3687
Description: Restricted "at most one" is preserved through implication (note wff reversal). (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Hypothesis
Ref Expression
rmoimia.1 (𝑥𝐴 → (𝜑𝜓))
Assertion
Ref Expression
rmoimia (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑)

Proof of Theorem rmoimia
StepHypRef Expression
1 rmoim 3686 . 2 (∀𝑥𝐴 (𝜑𝜓) → (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑))
2 rmoimia.1 . 2 (𝑥𝐴 → (𝜑𝜓))
31, 2mprg 3067 1 (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105  ∃*wrmo 3348
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1781  df-mo 2538  df-ral 3062  df-rmo 3349
This theorem is referenced by:  rmoimi  3688  2reu1  3841
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