Metamath Proof Explorer


Definition df-cnvrefs

Description: Define the class of all converse reflexive sets, see the comment of df-ssr . It is used only by df-cnvrefrels . (Contributed by Peter Mazsa, 22-Jul-2019)

Ref Expression
Assertion df-cnvrefs CnvRefs = x | I dom x × ran x S -1 x dom x × ran x

Detailed syntax breakdown

Step Hyp Ref Expression
0 ccnvrefs class CnvRefs
1 vx setvar x
2 cid class I
3 1 cv setvar x
4 3 cdm class dom x
5 3 crn class ran x
6 4 5 cxp class dom x × ran x
7 2 6 cin class I dom x × ran x
8 cssr class S
9 8 ccnv class S -1
10 3 6 cin class x dom x × ran x
11 7 10 9 wbr wff I dom x × ran x S -1 x dom x × ran x
12 11 1 cab class x | I dom x × ran x S -1 x dom x × ran x
13 0 12 wceq wff CnvRefs = x | I dom x × ran x S -1 x dom x × ran x