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Theorem nfmo1 1955
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 1947 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2 nfe1 1426 . . 3 𝑥𝑥𝜑
3 nfeu1 1954 . . 3 𝑥∃!𝑥𝜑
42, 3nfim 1505 . 2 𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
51, 4nfxfr 1404 1 𝑥∃*𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1390  wex 1422  ∃!weu 1943  ∃*wmo 1944
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-eu 1946  df-mo 1947
This theorem is referenced by:  moanmo  2020  euexex  2028  nfrmo1  2531  mob  2783  morex  2785  funimaexglem  5033
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