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Mirrors > Home > ILE Home > Th. List > qseq2 | Unicode version |
Description: Equality theorem for quotient set. (Contributed by NM, 23-Jul-1995.) |
Ref | Expression |
---|---|
qseq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eceq2 6517 | . . . . 5 | |
2 | 1 | eqeq2d 2169 | . . . 4 |
3 | 2 | rexbidv 2458 | . . 3 |
4 | 3 | abbidv 2275 | . 2 |
5 | df-qs 6486 | . 2 | |
6 | df-qs 6486 | . 2 | |
7 | 4, 5, 6 | 3eqtr4g 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 cab 2143 wrex 2436 cec 6478 cqs 6479 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 df-opab 4026 df-cnv 4594 df-dm 4596 df-rn 4597 df-res 4598 df-ima 4599 df-ec 6482 df-qs 6486 |
This theorem is referenced by: (None) |
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