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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 3615 |
. . 3
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2 | 1 | imaeq2d 4982 |
. 2
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3 | df-ec 6551 |
. 2
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4 | df-ec 6551 |
. 2
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5 | 2, 3, 4 | 3eqtr4g 2245 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-sn 3610 df-pr 3611 df-op 3613 df-br 4016 df-opab 4077 df-xp 4644 df-cnv 4646 df-dm 4648 df-rn 4649 df-res 4650 df-ima 4651 df-ec 6551 |
This theorem is referenced by: eceq1d 6585 ecelqsg 6602 snec 6610 qliftfun 6631 qliftfuns 6633 qliftval 6635 ecoptocl 6636 eroveu 6640 th3qlem1 6651 th3qlem2 6652 th3q 6654 dmaddpqlem 7390 nqpi 7391 1qec 7401 nqnq0 7454 nq0nn 7455 mulnnnq0 7463 addpinq1 7477 caucvgsrlemfv 7804 caucvgsr 7815 pitonnlem1 7858 axcaucvg 7913 divsfvalg 12767 |
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