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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 464 | . 2 |
4 | eqss 3082 | . 2 | |
5 | 3, 4 | syl6bbr 197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wss 3041 |
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-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 |
This theorem is referenced by: (None) |
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