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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 19020 | . 2 ⊢ Abel = (Grp ∩ CMnd) | |
2 | inss1 4117 | . 2 ⊢ (Grp ∩ CMnd) ⊆ Grp | |
3 | 1, 2 | eqsstri 3909 | 1 ⊢ Abel ⊆ Grp |
Colors of variables: wff setvar class |
Syntax hints: ∩ cin 3840 ⊆ wss 3841 Grpcgrp 18212 CMndccmn 19017 Abelcabl 19018 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1916 ax-6 1974 ax-7 2019 ax-8 2115 ax-9 2123 ax-ext 2710 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1545 df-ex 1787 df-sb 2074 df-clab 2717 df-cleq 2730 df-clel 2811 df-v 3399 df-in 3848 df-ss 3858 df-abl 19020 |
This theorem is referenced by: bj-ablssgrpel 35058 |
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