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Mirrors > Home > NFE Home > Th. List > cokeq2 | Unicode version |
Description: Equality theorem for Kuratowski composition of two classes. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
cokeq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvkeq 4216 |
. . . . 5
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2 | 1 | ins3keqd 4224 |
. . . 4
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3 | 2 | ineq2d 3458 |
. . 3
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4 | 3 | imakeq1d 4229 |
. 2
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5 | df-cok 4191 |
. 2
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6 | df-cok 4191 |
. 2
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7 | 4, 5, 6 | 3eqtr4g 2410 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-rex 2621 df-v 2862 df-nin 3212 df-compl 3213 df-in 3214 df-cnvk 4187 df-ins3k 4189 df-imak 4190 df-cok 4191 |
This theorem is referenced by: cokeq2i 4234 cokeq2d 4236 |
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