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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ablssgrp | Structured version Visualization version GIF version |
Description: Abelian groups are groups. (Contributed by BJ, 9-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-ablssgrp | ⊢ Abel ⊆ Grp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-abl 18242 | . 2 ⊢ Abel = (Grp ∩ CMnd) | |
2 | inss1 3866 | . 2 ⊢ (Grp ∩ CMnd) ⊆ Grp | |
3 | 1, 2 | eqsstri 3668 | 1 ⊢ Abel ⊆ Grp |
Colors of variables: wff setvar class |
Syntax hints: ∩ cin 3606 ⊆ wss 3607 Grpcgrp 17469 CMndccmn 18239 Abelcabl 18240 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-tru 1526 df-ex 1745 df-nf 1750 df-sb 1938 df-clab 2638 df-cleq 2644 df-clel 2647 df-nfc 2782 df-v 3233 df-in 3614 df-ss 3621 df-abl 18242 |
This theorem is referenced by: bj-ablssgrpel 33269 |
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