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Theorem mormo 2578
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 2017 . 2 (∃*𝑥𝜑 → ∃*𝑥(𝑥𝐴𝜑))
2 df-rmo 2367 . 2 (∃*𝑥𝐴 𝜑 ↔ ∃*𝑥(𝑥𝐴𝜑))
31, 2sylibr 132 1 (∃*𝑥𝜑 → ∃*𝑥𝐴 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wcel 1438  ∃*wmo 1949  ∃*wrmo 2362
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952  df-rmo 2367
This theorem is referenced by:  reueq  2814  reusv1  4280
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