Theorem nfmo1 2091

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 2083	. 2 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
2		nfe1 1545	. . 3 ⊢ Ⅎ𝑥∃𝑥𝜑
3		nfeu1 2090	. . 3 ⊢ Ⅎ𝑥∃!𝑥𝜑
4	2, 3	nfim 1621	. 2 ⊢ Ⅎ𝑥(∃𝑥𝜑 → ∃!𝑥𝜑)
5	1, 4	nfxfr 1523	1 ⊢ Ⅎ𝑥∃*𝑥𝜑

Syntax hints:   → wi 4  Ⅎwnf 1509  ∃wex 1541  ∃!weu 2079  ∃*wmo 2080

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-ial 1583  ax-i5r 1584

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-eu 2082  df-mo 2083

This theorem is referenced by:  moanmo  2157  euexex  2165  nfrmo1  2707  mob  2989  morex  2991  funimaexglem  5420