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Theorem nfmo 2046
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 1466 . . 3 𝑦
2 nfeu.1 . . . 4 𝑥𝜑
32a1i 9 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmod 2043 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54mptru 1362 1 𝑥∃*𝑦𝜑
Colors of variables: wff set class
Syntax hints:  wtru 1354  wnf 1460  ∃*wmo 2027
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030
This theorem is referenced by:  euexex  2111  nfdisjv  3989  reusv1  4454  mosubopt  4687  dffun6f  5224
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