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Mirrors > Home > ILE Home > Th. List > eceq1 | Unicode version |
Description: Equality theorem for equivalence class. (Contributed by NM, 23-Jul-1995.) |
Ref | Expression |
---|---|
eceq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sneq 3461 |
. . 3
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2 | 1 | imaeq2d 4787 |
. 2
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3 | df-ec 6308 |
. 2
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4 | df-ec 6308 |
. 2
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5 | 2, 3, 4 | 3eqtr4g 2146 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-sn 3456 df-pr 3457 df-op 3459 df-br 3852 df-opab 3906 df-xp 4457 df-cnv 4459 df-dm 4461 df-rn 4462 df-res 4463 df-ima 4464 df-ec 6308 |
This theorem is referenced by: eceq1d 6342 ecelqsg 6359 snec 6367 qliftfun 6388 qliftfuns 6390 qliftval 6392 ecoptocl 6393 eroveu 6397 th3qlem1 6408 th3qlem2 6409 th3q 6411 dmaddpqlem 6990 nqpi 6991 1qec 7001 nqnq0 7054 nq0nn 7055 mulnnnq0 7063 addpinq1 7077 caucvgsrlemfv 7390 caucvgsr 7401 pitonnlem1 7436 axcaucvg 7489 |
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