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Mirrors > Home > ILE Home > Th. List > ectocld | Unicode version |
Description: Implicit substitution of class for equivalence class. (Contributed by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
ectocl.1 |
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ectocl.2 |
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ectocld.3 |
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Ref | Expression |
---|---|
ectocld |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elqsi 6521 |
. . . 4
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2 | ectocl.1 |
. . . 4
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3 | 1, 2 | eleq2s 2249 |
. . 3
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4 | ectocld.3 |
. . . . 5
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5 | ectocl.2 |
. . . . . 6
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6 | 5 | eqcoms 2157 |
. . . . 5
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7 | 4, 6 | syl5ibcom 154 |
. . . 4
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8 | 7 | rexlimdva 2571 |
. . 3
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9 | 3, 8 | syl5 32 |
. 2
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10 | 9 | imp 123 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-10 1482 ax-11 1483 ax-i12 1484 ax-bndl 1486 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-ext 2136 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1740 df-clab 2141 df-cleq 2147 df-clel 2150 df-nfc 2285 df-ral 2437 df-rex 2438 df-v 2711 df-qs 6475 |
This theorem is referenced by: ectocl 6536 elqsn0m 6537 qsel 6546 |
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