Theorem nfmov 2594

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2596 for a version without disjoint variable conditions but requiring ax-13 2410. (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 1831	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmov.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmodv 2593	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1574	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1568  Ⅎwnf 1810  ∃*wmo 2571

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-10 2182  ax-11 2198  ax-12 2219

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1570  df-ex 1807  df-nf 1811  df-mo 2573

This theorem is referenced by:  mo3  2598  2moexv  2661  moexexvw  2662  2moswapv  2663  2euexv  2665  2mo  2682  nfrmow  3405  reusv1  5366  reusv2lem1  5367  mosubopt  5491  dffun6f  6548