Metamath Proof Explorer


Definition df-dom

Description: Define the dominance relation. For an alternate definition see dfdom2 . Compare Definition of Enderton p. 145. Typical textbook definitions are derived as brdom and domen . (Contributed by NM, 28-Mar-1998)

Ref Expression
Assertion df-dom =xy|ff:x1-1y

Detailed syntax breakdown

Step Hyp Ref Expression
0 cdom class
1 vx setvarx
2 vy setvary
3 vf setvarf
4 3 cv setvarf
5 1 cv setvarx
6 2 cv setvary
7 5 6 4 wf1 wfff:x1-1y
8 7 3 wex wffff:x1-1y
9 8 1 2 copab classxy|ff:x1-1y
10 0 9 wceq wff=xy|ff:x1-1y