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Theorem 2mo2 2372
 Description: This theorem extends the idea of "at most one" to expressions in two set variables ("at most one pair and ". Note: this is not expressed by ). 2eu4 2380 relates this extension to double existential uniqueness, if at least one pair exists. (Contributed by Wolf Lammen, 26-Oct-2019.)
Assertion
Ref Expression
2mo2
Distinct variable groups:   ,,,   ,,

Proof of Theorem 2mo2
StepHypRef Expression
1 eeanv 1988 . 2
2 jcab 863 . . . . 5
322albii 1641 . . . 4
4 19.26-2 1681 . . . 4
5 19.23v 1760 . . . . . 6
65albii 1640 . . . . 5
7 alcom 1845 . . . . . 6
8 19.23v 1760 . . . . . . 7
98albii 1640 . . . . . 6
107, 9bitri 249 . . . . 5
116, 10anbi12i 697 . . . 4
123, 4, 113bitri 271 . . 3
13122exbii 1668 . 2
14 mo2v 2289 . . 3
15 mo2v 2289 . . 3
1614, 15anbi12i 697 . 2
171, 13, 163bitr4ri 278 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  E*wmo 2283 This theorem is referenced by:  2mo  2373  2moOLD  2374  2eu4  2380 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-11 1842  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287
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