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Theorem nfmo1 2485
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 2479 . 2 (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2 nfe1 2029 . . 3 𝑥𝑥𝜑
3 nfeu1 2484 . . 3 𝑥∃!𝑥𝜑
42, 3nfim 1827 . 2 𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
51, 4nfxfr 1777 1 𝑥∃*𝑥𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1701  wnf 1705  ∃!weu 2474  ∃*wmo 2475
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-10 2021  ax-11 2036  ax-12 2049
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707  df-eu 2478  df-mo 2479
This theorem is referenced by:  mo3  2511  moanmo  2536  mopick2  2544  moexex  2545  2mo  2555  2eu3  2559  nfrmo1  3106  mob  3375  morex  3377  wl-mo3t  32985
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