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Mirrors > Home > ILE Home > Th. List > seeq1 | Unicode version |
Description: Equality theorem for the set-like predicate. (Contributed by Mario Carneiro, 24-Jun-2015.) |
Ref | Expression |
---|---|
seeq1 | Se Se |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss2 3183 | . . 3 | |
2 | sess1 4300 | . . 3 Se Se | |
3 | 1, 2 | syl 14 | . 2 Se Se |
4 | eqimss 3182 | . . 3 | |
5 | sess1 4300 | . . 3 Se Se | |
6 | 4, 5 | syl 14 | . 2 Se Se |
7 | 3, 6 | impbid 128 | 1 Se Se |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1335 wss 3102 Se wse 4292 |
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 ax-sep 4085 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rab 2444 df-v 2714 df-in 3108 df-ss 3115 df-br 3968 df-se 4296 |
This theorem is referenced by: (None) |
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