Theorem nfmo1 2089

Description: Bound-variable hypothesis builder for "at most one". (Contributed by NM, 8-Mar-1995.) (Revised by Mario Carneiro, 7-Oct-2016.)

Assertion

Ref	Expression
nfmo1	⊢ Ⅎ𝑥∃*𝑥𝜑

Proof of Theorem nfmo1

Step	Hyp	Ref	Expression
1		df-mo 2081	. 2 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2		nfe1 1542	. . 3 ⊢ Ⅎ𝑥∃𝑥𝜑
3		nfeu1 2088	. . 3 ⊢ Ⅎ𝑥∃!𝑥𝜑
4	2, 3	nfim 1618	. 2 ⊢ Ⅎ𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
5	1, 4	nfxfr 1520	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  Ⅎwnf 1506  ∃wex 1538  ∃!weu 2077  ∃*wmo 2078

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-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-ial 1580  ax-i5r 1581

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-eu 2080  df-mo 2081

This theorem is referenced by:  moanmo  2155  euexex  2163  nfrmo1  2704  mob  2985  morex  2987  funimaexglem  5403