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Theorem nfmo1 2509
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 2503 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2 nfe1 2067 . . 3 𝑥𝑥𝜑
3 nfeu1 2508 . . 3 𝑥∃!𝑥𝜑
42, 3nfim 1865 . 2 𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
51, 4nfxfr 1819 1 𝑥∃*𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1744  wnf 1748  ∃!weu 2498  ∃*wmo 2499
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-11 2074  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1745  df-nf 1750  df-eu 2502  df-mo 2503
This theorem is referenced by:  mo3  2536  moanmo  2561  mopick2  2569  moexex  2570  2mo  2580  2eu3  2584  nfrmo1  3140  mob  3421  morex  3423  wl-mo3t  33488
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