Theorem nfmo1 2031

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 2023	. 2 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2		nfe1 1489	. . 3 ⊢ Ⅎ𝑥∃𝑥𝜑
3		nfeu1 2030	. . 3 ⊢ Ⅎ𝑥∃!𝑥𝜑
4	2, 3	nfim 1565	. 2 ⊢ Ⅎ𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
5	1, 4	nfxfr 1467	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  Ⅎwnf 1453  ∃wex 1485  ∃!weu 2019  ∃*wmo 2020

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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-eu 2022  df-mo 2023

This theorem is referenced by:  moanmo  2096  euexex  2104  nfrmo1  2642  mob  2912  morex  2914  funimaexglem  5281