Theorem nfmo1 2026

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 2018	. 2 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2		nfe1 1484	. . 3 ⊢ Ⅎ𝑥∃𝑥𝜑
3		nfeu1 2025	. . 3 ⊢ Ⅎ𝑥∃!𝑥𝜑
4	2, 3	nfim 1560	. 2 ⊢ Ⅎ𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
5	1, 4	nfxfr 1462	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  Ⅎwnf 1448  ∃wex 1480  ∃!weu 2014  ∃*wmo 2015

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-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-eu 2017  df-mo 2018

This theorem is referenced by:  moanmo  2091  euexex  2099  nfrmo1  2638  mob  2908  morex  2910  funimaexglem  5271