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Theorem nfmo 2556
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
nfeu.1 𝑥𝜑
Assertion
Ref Expression
nfmo 𝑥∃*𝑦𝜑

Proof of Theorem nfmo
StepHypRef Expression
1 nftru 1811 . . 3 𝑦
2 nfeu.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmod 2554 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54trud 1574 1 𝑥∃*𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1565  wnf 1789  ∃*wmo 2540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1818  ax-5 1920  ax-6 1986  ax-7 2022  ax-10 2100  ax-11 2115  ax-12 2128  ax-13 2323
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1567  df-ex 1786  df-nf 1791  df-eu 2543  df-mo 2544
This theorem is referenced by:  mo3  2577  moexex  2611  2moex  2613  2euex  2614  2mo  2621  reusv1  4939  reusv1OLD  4940  reusv2lem1  4941  mosubopt  5044  dffun6f  5983
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