Theorem nfmo 2578

Description: Bound-variable hypothesis builder for the at-most-one quantifier. Note that 𝑥 and 𝑦 need not be disjoint. (Contributed by NM, 9-Mar-1995.)

Hypothesis

Ref	Expression
nfmo.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfmo	⊢ Ⅎ𝑥∃*𝑦𝜑

Proof of Theorem nfmo

Step	Hyp	Ref	Expression
1		nftru 1899	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmo.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmod 2577	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1660	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1653  Ⅎwnf 1878  ∃*wmo 2562

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2069  ax-7 2105  ax-10 2183  ax-11 2198  ax-12 2211  ax-13 2349

This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-mo 2564

This theorem is referenced by:  mo3  2627  moexex  2662  2moex  2664  2euex  2665  2mo  2672  reusv1  5031  reusv2lem1  5032  mosubopt  5130  dffun6f  6081