Theorem nfmo 2556

Description: Bound-variable hypothesis builder for the at-most-one quantifier. Note that 𝑥 and 𝑦 need not be disjoint. Usage of this theorem is discouraged because it depends on ax-13 2371. Use the weaker nfmov 2554 when possible. (Contributed by NM, 9-Mar-1995.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfmo.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfmo	⊢ Ⅎ𝑥∃*𝑦𝜑

Proof of Theorem nfmo

Step	Hyp	Ref	Expression
1		nftru 1805	. . 3 ⊢ Ⅎ𝑦⊤
2		nfmo.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmod 2555	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1548	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1542  Ⅎwnf 1784  ∃*wmo 2532

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-10 2143  ax-11 2159  ax-12 2179  ax-13 2371

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-nf 1785  df-mo 2534

This theorem is referenced by:  moexex  2632  2moex  2634  2euex  2635