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Theorem nfmo 1920
 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 1355 . . 3 𝑦
2 nfeu.1 . . . 4 𝑥𝜑
32a1i 9 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmod 1917 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54trud 1252 1 𝑥∃*𝑦𝜑
 Colors of variables: wff set class Syntax hints:  ⊤wtru 1244  Ⅎwnf 1349  ∃*wmo 1901 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904 This theorem is referenced by:  euexex  1985  nfdisjv  3757  reusv1  4190  mosubopt  4405  dffun6f  4915
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