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Mirrors > Home > ILE Home > Th. List > elprg | Unicode version |
Description: A member of an unordered pair of classes is one or the other of them. Exercise 1 of [TakeutiZaring] p. 15, generalized. (Contributed by NM, 13-Sep-1995.) |
Ref | Expression |
---|---|
elprg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2119 |
. . 3
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2 | eqeq1 2119 |
. . 3
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3 | 1, 2 | orbi12d 765 |
. 2
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4 | dfpr2 3510 |
. 2
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5 | 3, 4 | elab2g 2798 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-tru 1315 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-v 2657 df-un 3039 df-sn 3497 df-pr 3498 |
This theorem is referenced by: elpr 3512 elpr2 3513 elpri 3514 eltpg 3533 prid1g 3591 preqr1g 3657 m1expeven 10227 maxclpr 10880 minmax 10887 minclpr 10894 xrminmax 10920 |
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