Theorem nfmo 2058

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 1477	. . 3 ⊢ Ⅎ𝑦⊤
2		nfeu.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 9	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfmod 2055	. 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑)
5	4	mptru 1373	1 ⊢ Ⅎ𝑥∃*𝑦𝜑

Syntax hints:  ⊤wtru 1365  Ⅎwnf 1471  ∃*wmo 2039

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042

This theorem is referenced by:  euexex  2123  nfdisjv  4010  reusv1  4479  mosubopt  4712  dffun6f  5251