Theorem nfmov 2557

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2559 for a version without disjoint variable conditions but requiring ax-13 2374. (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 1800	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmov.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmodv 2556	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1543	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1537  Ⅎwnf 1779  ∃*wmo 2535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-10 2138  ax-11 2154  ax-12 2174

This theorem depends on definitions:  df-bi 207  df-or 848  df-tru 1539  df-ex 1776  df-nf 1780  df-mo 2537

This theorem is referenced by:  mo3  2561  2moexv  2624  moexexvw  2625  2moswapv  2626  2euexv  2628  2mo  2645  nfrmow  3410  reusv1  5402  reusv2lem1  5403  mosubopt  5519  dffun6f  6580