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Theorem 2mo2 2379
 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 2385 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:   ,,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem 2mo2
StepHypRef Expression
1 eeanv 2078 . 2
2 jcab 874 . . . . 5
322albii 1692 . . . 4
4 19.26-2 1733 . . . 4
5 19.23v 1818 . . . . . 6
65albii 1691 . . . . 5
7 alcom 1923 . . . . . 6
8 19.23v 1818 . . . . . . 7
98albii 1691 . . . . . 6
107, 9bitri 253 . . . . 5
116, 10anbi12i 703 . . . 4
123, 4, 113bitri 275 . . 3
13122exbii 1719 . 2
14 mo2v 2306 . . 3
15 mo2v 2306 . . 3
1614, 15anbi12i 703 . 2
171, 13, 163bitr4ri 282 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371  wal 1442  wex 1663  wmo 2300 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668  df-eu 2303  df-mo 2304 This theorem is referenced by:  2mo  2380  2eu4  2385
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