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Theorem mormo 3135
 Description: Unrestricted "at most one" implies restricted "at most one". (Contributed by NM, 16-Jun-2017.)
Assertion
Ref Expression
mormo (∃*𝑥𝜑 → ∃*𝑥𝐴 𝜑)

Proof of Theorem mormo
StepHypRef Expression
1 moan 2512 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝑥𝐴𝜑))
2 df-rmo 2904 . 2 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥(𝑥𝐴𝜑))
31, 2sylibr 223 1 (∃*𝑥𝜑 → ∃*𝑥𝐴 𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∈ wcel 1977  ∃*wmo 2459  ∃*wrmo 2899 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463  df-rmo 2904 This theorem is referenced by:  reueq  3371  reusv1  4792  reusv1OLD  4793  brdom4  9233  phpreu  32563
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