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Theorem mormo 3307
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 2673 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝑥𝐴𝜑))
2 df-rmo 3069 . 2 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥(𝑥𝐴𝜑))
31, 2sylibr 224 1 (∃*𝑥𝜑 → ∃*𝑥𝐴 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wcel 2145  ∃*wmo 2619  ∃*wrmo 3064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-ex 1853  df-nf 1858  df-eu 2622  df-mo 2623  df-rmo 3069
This theorem is referenced by:  reueq  3556  reusv1  4997  brdom4  9554  phpreu  33726
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