Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
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 18911 | . 2 ⊢ Abel = (Grp ∩ CMnd) | |
2 | inss1 4207 | . 2 ⊢ (Grp ∩ CMnd) ⊆ Grp | |
3 | 1, 2 | eqsstri 4003 | 1 ⊢ Abel ⊆ Grp |
Colors of variables: wff setvar class |
Syntax hints: ∩ cin 3937 ⊆ wss 3938 Grpcgrp 18105 CMndccmn 18908 Abelcabl 18909 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-v 3498 df-in 3945 df-ss 3954 df-abl 18911 |
This theorem is referenced by: bj-ablssgrpel 34561 |
Copyright terms: Public domain | W3C validator |