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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 2184 |
. . 3
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2 | eqeq1 2184 |
. . 3
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3 | 1, 2 | orbi12d 793 |
. 2
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4 | dfpr2 3610 |
. 2
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5 | 3, 4 | elab2g 2884 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-sn 3597 df-pr 3598 |
This theorem is referenced by: elpr 3612 elpr2 3613 elpri 3614 eldifpr 3618 eltpg 3636 prid1g 3695 preqr1g 3764 m1expeven 10540 maxclpr 11202 minmax 11209 minclpr 11216 xrminmax 11244 lgslem1 14034 lgsval 14038 lgsfvalg 14039 lgsfcl2 14040 lgsval2lem 14044 lgsdir2lem4 14065 lgsdir2lem5 14066 lgsdir2 14067 lgsne0 14072 |
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