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Theorem nfmo1 1957
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfmo1 𝑥∃*𝑥𝜑

Proof of Theorem nfmo1
StepHypRef Expression
1 df-mo 1949 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2 nfe1 1428 . . 3 𝑥𝑥𝜑
3 nfeu1 1956 . . 3 𝑥∃!𝑥𝜑
42, 3nfim 1507 . 2 𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
51, 4nfxfr 1406 1 𝑥∃*𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1392  wex 1424  ∃!weu 1945  ∃*wmo 1946
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-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-ial 1470  ax-i5r 1471
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-eu 1948  df-mo 1949
This theorem is referenced by:  moanmo  2022  euexex  2030  nfrmo1  2535  mob  2788  morex  2790  funimaexglem  5058
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