Theorem nfmov 2579

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo 2581 for a version without disjoint variable conditions but requiring ax-13 2380. (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 1807	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmov.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmodv 2578	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1546	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1540  Ⅎwnf 1786  ∃*wmo 2556

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-10 2143  ax-11 2159  ax-12 2176

This theorem depends on definitions:  df-bi 210  df-or 846  df-tru 1542  df-ex 1783  df-nf 1787  df-mo 2558

This theorem is referenced by:  mo3  2583  2moexv  2649  moexexvw  2650  2moswapv  2651  2euexv  2653  2mo  2670  reusv1  5267  reusv2lem1  5268  mosubopt  5370  dffun6f  6350