Theorem nfmov 2588

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2590 for a version without disjoint variable conditions but requiring ax-13 2404. (Contributed by NM, 9-Mar-1995.) (Revised by Wolf Lammen, 2-Oct-2023.)

Hypothesis

Ref	Expression
nfmov.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfmov	⊢ Ⅎ𝑥∃*𝑦𝜑

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥, 𝑦)

Proof of Theorem nfmov

Step	Hyp	Ref	Expression
1		nftru 1837	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmov.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmodv 2587	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1577	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

This proof depends on syntax axioms:  ⊤wtru 1571  Ⅎwnf 1816  ∃*wmo 2565

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-10 2180  ax-11 2197  ax-12 2216

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-nf 1817  df-mo 2567

This theorem is used by:  mo3  2592  2moexv  2655  moexexvw  2656  2moswapv  2657  2euexv  2659  2mo  2676  nfrmow  3398  reusv1  5366  reusv2lem1  5367  mosubopt  5489  mosubott  5491  dffun6f  6581