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Theorem mormo 3370
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 2541 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝑥𝐴𝜑))
2 df-rmo 3365 . 2 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥(𝑥𝐴𝜑))
31, 2sylibr 233 1 (∃*𝑥𝜑 → ∃*𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 394  wcel 2099  ∃*wmo 2527  ∃*wrmo 3364
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804
This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1775  df-mo 2529  df-rmo 3365
This theorem is referenced by:  reueq  3731  reusv1  5392  brdom4  10562  phpreu  37316
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