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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 | |
ectocl.2 | |
ectocld.3 |
Ref | Expression |
---|---|
ectocld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elqsi 6561 | . . . 4 | |
2 | ectocl.1 | . . . 4 | |
3 | 1, 2 | eleq2s 2265 | . . 3 |
4 | ectocld.3 | . . . . 5 | |
5 | ectocl.2 | . . . . . 6 | |
6 | 5 | eqcoms 2173 | . . . . 5 |
7 | 4, 6 | syl5ibcom 154 | . . . 4 |
8 | 7 | rexlimdva 2587 | . . 3 |
9 | 3, 8 | syl5 32 | . 2 |
10 | 9 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wcel 2141 wrex 2449 cec 6507 cqs 6508 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-qs 6515 |
This theorem is referenced by: ectocl 6576 elqsn0m 6577 qsel 6586 |
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