Theorem nfmo1 1909

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 1901	. 2 ⊢ (∃*xφ ↔ (∃xφ → ∃!xφ))
2		nfe1 1382	. . 3 ⊢ Ⅎx∃xφ
3		nfeu1 1908	. . 3 ⊢ Ⅎx∃!xφ
4	2, 3	nfim 1461	. 2 ⊢ Ⅎx(∃xφ → ∃!xφ)
5	1, 4	nfxfr 1360	1 ⊢ Ⅎx∃*xφ

Syntax hints:   → wi 4  Ⅎwnf 1346  ∃wex 1378  ∃!weu 1897  ∃*wmo 1898

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424  ax-i5r 1425

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-eu 1900  df-mo 1901

This theorem is referenced by:  moanmo  1974  euexex  1982  nfrmo1  2476  mob  2717  morex  2719  funimaexglem  4925