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Theorem nfmo 2058
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 1477 . . 3 𝑦
2 nfeu.1 . . . 4 𝑥𝜑
32a1i 9 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmod 2055 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54mptru 1373 1 𝑥∃*𝑦𝜑
Colors of variables: wff set class
Syntax hints:  wtru 1365  wnf 1471  ∃*wmo 2039
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042
This theorem is referenced by:  euexex  2123  nfdisjv  4010  reusv1  4479  mosubopt  4712  dffun6f  5251
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