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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 2196 |
. . 3
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2 | eqeq1 2196 |
. . 3
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3 | 1, 2 | orbi12d 794 |
. 2
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4 | dfpr2 3626 |
. 2
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5 | 3, 4 | elab2g 2899 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-un 3148 df-sn 3613 df-pr 3614 |
This theorem is referenced by: elpr 3628 elpr2 3629 elpri 3630 eldifpr 3634 eltpg 3652 prid1g 3711 preqr1g 3781 m1expeven 10601 maxclpr 11266 minmax 11273 minclpr 11280 xrminmax 11308 lgslem1 14879 lgsval 14883 lgsfvalg 14884 lgsfcl2 14885 lgsval2lem 14889 lgsdir2lem4 14910 lgsdir2lem5 14911 lgsdir2 14912 lgsne0 14917 |
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