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Theorem nfmov 2560
Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2562 for a version without disjoint variable conditions but requiring ax-13 2377. (Contributed by NM, 9-Mar-1995.) (Revised by Wolf Lammen, 2-Oct-2023.)
Hypothesis
Ref Expression
nfmov.1 𝑥𝜑
Assertion
Ref Expression
nfmov 𝑥∃*𝑦𝜑
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfmov
StepHypRef Expression
1 nftru 1804 . . 3 𝑦
2 nfmov.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmodv 2559 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54mptru 1547 1 𝑥∃*𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1541  wnf 1783  ∃*wmo 2538
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-10 2141  ax-11 2157  ax-12 2177
This theorem depends on definitions:  df-bi 207  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-mo 2540
This theorem is referenced by:  mo3  2564  2moexv  2627  moexexvw  2628  2moswapv  2629  2euexv  2631  2mo  2648  nfrmow  3413  reusv1  5397  reusv2lem1  5398  mosubopt  5515  dffun6f  6579
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