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Definition df-subg 14929
 Description: Define a subgroup of a group as a set of elements that is a group in its own right. Equivalently (issubg2 14947), a subgroup is a subset of the group that is closed for the group internal operation (see subgcl 14942), contains the neutral element of the group (see subg0 14938) and contains the inverses for all of its elements (see subginvcl 14941). (Contributed by Mario Carneiro, 2-Dec-2014.)
Assertion
Ref Expression
df-subg SubGrp s
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-subg
StepHypRef Expression
1 csubg 14926 . 2 SubGrp
2 vw . . 3
3 cgrp 14673 . . 3
42cv 1651 . . . . . 6
5 vs . . . . . . 7
65cv 1651 . . . . . 6
7 cress 13458 . . . . . 6 s
84, 6, 7co 6072 . . . . 5 s
98, 3wcel 1725 . . . 4 s
10 cbs 13457 . . . . . 6
114, 10cfv 5445 . . . . 5
1211cpw 3791 . . . 4
139, 5, 12crab 2701 . . 3 s
142, 3, 13cmpt 4258 . 2 s
151, 14wceq 1652 1 SubGrp s
 Colors of variables: wff set class This definition is referenced by:  issubg  14932
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