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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-sseq | Unicode version |
Description: If two converse inclusions are characterized each by a formula, then equality is characterized by the conjunction of these formulas. (Contributed by BJ, 30-Nov-2019.) |
Ref | Expression |
---|---|
bj-sseq.1 | |
bj-sseq.2 |
Ref | Expression |
---|---|
bj-sseq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-sseq.1 | . . 3 | |
2 | bj-sseq.2 | . . 3 | |
3 | 1, 2 | anbi12d 456 | . 2 |
4 | eqss 3014 | . 2 | |
5 | 3, 4 | syl6bbr 196 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wss 2973 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-in 2979 df-ss 2986 |
This theorem is referenced by: (None) |
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