Theorem nfmo1 2215

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 2209	. 2 ⊢ (∃*xφ ↔ (∃xφ → ∃!xφ))
2		nfe1 1732	. . 3 ⊢ Ⅎx∃xφ
3		nfeu1 2214	. . 3 ⊢ Ⅎx∃!xφ
4	2, 3	nfim 1813	. 2 ⊢ Ⅎx(∃xφ → ∃!xφ)
5	1, 4	nfxfr 1570	1 ⊢ Ⅎx∃*xφ

Syntax hints:   → wi 4  ∃wex 1541  Ⅎwnf 1544  ∃!weu 2204  ∃*wmo 2205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-eu 2208  df-mo 2209

This theorem is referenced by:  moanmo  2264  mopick2  2271  moexex  2273  2eu3  2286  nfrmo1  2783  mob  3019  morex  3021