Theorem mopick 2356

Description: "At most one" picks a variable value, eliminating an existential quantifier. (Contributed by NM, 27-Jan-1997.) (Proof shortened by Wolf Lammen, 17-Sep-2019.)

Assertion

Ref	Expression
mopick

Proof of Theorem mopick

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		mo2v 2289	. . 3
2		sp 1859	. . . . 5
3		pm3.45 834	. . . . . . 7
4	3	aleximi 1653	. . . . . 6
5		sb56 2172	. . . . . . 7
6		sp 1859	. . . . . . 7
7	5, 6	sylbi 195	. . . . . 6
8	4, 7	syl6 33	. . . . 5
9	2, 8	syl5d 67	. . . 4
10	9	exlimiv 1722	. . 3
11	1, 10	sylbi 195	. 2
12	11	imp 429	1

Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  E*wmo 2283

This theorem is referenced by:  eupick  2358  mopick2  2362  moexex  2363  morex  3283  imadif  5668  cmetss  21753

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287