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Theorem nfmo 1968
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 1400 . . 3 𝑦
2 nfeu.1 . . . 4 𝑥𝜑
32a1i 9 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmod 1965 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54mptru 1298 1 𝑥∃*𝑦𝜑
Colors of variables: wff set class
Syntax hints:  wtru 1290  wnf 1394  ∃*wmo 1949
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-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952
This theorem is referenced by:  euexex  2033  nfdisjv  3834  reusv1  4280  mosubopt  4503  dffun6f  5028
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