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Theorem nfmo1 1928
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 1920 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2 nfe1 1401 . . 3 𝑥𝑥𝜑
3 nfeu1 1927 . . 3 𝑥∃!𝑥𝜑
42, 3nfim 1480 . 2 𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
51, 4nfxfr 1379 1 𝑥∃*𝑥𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1365  wex 1397  ∃!weu 1916  ∃*wmo 1917
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443  ax-i5r 1444
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-eu 1919  df-mo 1920
This theorem is referenced by:  moanmo  1993  euexex  2001  nfrmo1  2499  mob  2745  morex  2747  funimaexglem  5009
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