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Theorem nfmov 2641
Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2643 for a version without disjoint variable conditions but requiring ax-13 2385. (Contributed 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 1798 . . 3 𝑦
2 nfmov.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmodv 2640 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54mptru 1537 1 𝑥∃*𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1531  wnf 1777  ∃*wmo 2617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-10 2138  ax-11 2153  ax-12 2169
This theorem depends on definitions:  df-bi 208  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-mo 2619
This theorem is referenced by:  mo3  2645  2moexv  2710  moexexvw  2711  2moswapv  2712  2euexv  2714  2mo  2731  reusv1  5293  reusv2lem1  5294  mosubopt  5396  dffun6f  6365
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