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Mirrors > Home > MPE Home > Th. List > clel2 | Structured version Visualization version Unicode version |
Description: An alternate definition of class membership when the class is a set. (Contributed by NM, 18-Aug-1993.) |
Ref | Expression |
---|---|
clel2.1 |
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Ref | Expression |
---|---|
clel2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clel2.1 |
. . 3
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2 | eleq1 2537 |
. . 3
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3 | 1, 2 | ceqsalv 3061 |
. 2
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4 | 3 | bicomi 207 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-12 1950 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-v 3033 |
This theorem is referenced by: snss 4087 mptelee 25004 |
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