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Theorem nfmov 2579
 Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2581 for a version without disjoint variable conditions but requiring ax-13 2380. (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 1807 . . 3 𝑦
2 nfmov.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmodv 2578 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54mptru 1546 1 𝑥∃*𝑦𝜑
 Colors of variables: wff setvar class Syntax hints:  ⊤wtru 1540  Ⅎwnf 1786  ∃*wmo 2556 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-10 2143  ax-11 2159  ax-12 2176 This theorem depends on definitions:  df-bi 210  df-or 846  df-tru 1542  df-ex 1783  df-nf 1787  df-mo 2558 This theorem is referenced by:  mo3  2583  2moexv  2649  moexexvw  2650  2moswapv  2651  2euexv  2653  2mo  2670  reusv1  5267  reusv2lem1  5268  mosubopt  5370  dffun6f  6350
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