Theorem nfmo 2019

Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 9-Mar-1995.)

Hypothesis

Ref	Expression
nfeu.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfmo	⊢ Ⅎ𝑥∃*𝑦𝜑

Proof of Theorem nfmo

Step	Hyp	Ref	Expression
1		nftru 1442	. . 3 ⊢ Ⅎ𝑦⊤
2		nfeu.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 9	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmod 2016	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1340	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1332  Ⅎwnf 1436  ∃*wmo 2000

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003

This theorem is referenced by:  euexex  2084  nfdisjv  3918  reusv1  4379  mosubopt  4604  dffun6f  5136