Theorem nfmov 2554

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2556 for a version without disjoint variable conditions but requiring ax-13 2371. (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 1804	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmov.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmodv 2553	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1547	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1541  Ⅎwnf 1783  ∃*wmo 2532

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-10 2142  ax-11 2158  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-or 848  df-tru 1543  df-ex 1780  df-nf 1784  df-mo 2534

This theorem is referenced by:  mo3  2558  2moexv  2621  moexexvw  2622  2moswapv  2623  2euexv  2625  2mo  2642  nfrmow  3387  reusv1  5355  reusv2lem1  5356  mosubopt  5473  dffun6f  6532