Theorem nfmov 2619

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2621 for a version without disjoint variable conditions but requiring ax-13 2379. (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 1806	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmov.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmodv 2618	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1545	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1539  Ⅎwnf 1785  ∃*wmo 2596

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-11 2158  ax-12 2175

This theorem depends on definitions:  df-bi 210  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-mo 2598

This theorem is referenced by:  mo3  2623  2moexv  2689  moexexvw  2690  2moswapv  2691  2euexv  2693  2mo  2710  reusv1  5263  reusv2lem1  5264  mosubopt  5365  dffun6f  6338