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Theorem nfmod 1992
Description: Bound-variable hypothesis builder for "at most one." (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypotheses
Ref Expression
nfeud.1 𝑦𝜑
nfeud.2 (𝜑 → Ⅎ𝑥𝜓)
Assertion
Ref Expression
nfmod (𝜑 → Ⅎ𝑥∃*𝑦𝜓)

Proof of Theorem nfmod
StepHypRef Expression
1 df-mo 1979 . 2 (∃*𝑦𝜓 ↔ (∃𝑦𝜓 → ∃!𝑦𝜓))
2 nfeud.1 . . . 4 𝑦𝜑
3 nfeud.2 . . . 4 (𝜑 → Ⅎ𝑥𝜓)
42, 3nfexd 1717 . . 3 (𝜑 → Ⅎ𝑥𝑦𝜓)
52, 3nfeud 1991 . . 3 (𝜑 → Ⅎ𝑥∃!𝑦𝜓)
64, 5nfimd 1547 . 2 (𝜑 → Ⅎ𝑥(∃𝑦𝜓 → ∃!𝑦𝜓))
71, 6nfxfrd 1434 1 (𝜑 → Ⅎ𝑥∃*𝑦𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1419  wex 1451  ∃!weu 1975  ∃*wmo 1976
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979
This theorem is referenced by:  nfmo  1995
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