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Mirrors > Home > MPE Home > Th. List > eltp | Structured version Visualization version Unicode version |
Description: A member of an unordered triple of classes is one of them. Special case of Exercise 1 of [TakeutiZaring] p. 17. (Contributed by NM, 8-Apr-1994.) (Revised by Mario Carneiro, 11-Feb-2015.) |
Ref | Expression |
---|---|
eltp.1 |
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Ref | Expression |
---|---|
eltp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eltp.1 |
. 2
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2 | eltpg 4016 |
. 2
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3 | 1, 2 | ax-mp 5 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 987 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-v 3049 df-un 3411 df-sn 3971 df-pr 3973 df-tp 3975 |
This theorem is referenced by: dftp2 4020 tpid1 4088 tpid2 4089 tpid3 4091 tpres 6122 bpoly3 14123 nb3graprlem1 25191 frgra3vlem1 25740 frgra3vlem2 25741 brtp 30401 sltsolem1 30569 nb3grprlem1 39464 |
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