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Theorem rmoimia 3537
 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 3536 . 2 (∀𝑥𝐴 (𝜑𝜓) → (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑))
2 rmoimia.1 . 2 (𝑥𝐴 → (𝜑𝜓))
31, 2mprg 3052 1 (∃*𝑥𝐴 𝜓 → ∃*𝑥𝐴 𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2127  ∃*wrmo 3041 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1859  ax-4 1874  ax-5 1976  ax-6 2042  ax-7 2078  ax-10 2156  ax-12 2184 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1842  df-nf 1847  df-eu 2599  df-mo 2600  df-ral 3043  df-rmo 3046 This theorem is referenced by:  rmoimi  41651  2reu1  41661
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