Theorem nfmov 2586

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2588 for a version without disjoint variable conditions but requiring ax-13 2402. (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 1823	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmov.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmodv 2585	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1566	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1560  Ⅎwnf 1802  ∃*wmo 2563

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-10 2174  ax-11 2190  ax-12 2211

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1562  df-ex 1799  df-nf 1803  df-mo 2565

This theorem is referenced by:  mo3  2590  2moexv  2653  moexexvw  2654  2moswapv  2655  2euexv  2657  2mo  2674  nfrmow  3395  reusv1  5351  reusv2lem1  5352  mosubopt  5476  dffun6f  6531