Theorem nfmo1 2054

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 2046	. 2 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2		nfe1 1507	. . 3 ⊢ Ⅎ𝑥∃𝑥𝜑
3		nfeu1 2053	. . 3 ⊢ Ⅎ𝑥∃!𝑥𝜑
4	2, 3	nfim 1583	. 2 ⊢ Ⅎ𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
5	1, 4	nfxfr 1485	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  Ⅎwnf 1471  ∃wex 1503  ∃!weu 2042  ∃*wmo 2043

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-eu 2045  df-mo 2046

This theorem is referenced by:  moanmo  2119  euexex  2127  nfrmo1  2667  mob  2942  morex  2944  funimaexglem  5337