Metamath Proof Explorer


Theorem rankid

Description: Identity law for the rank function. (Contributed by NM, 3-Oct-2003) (Revised by Mario Carneiro, 17-Nov-2014)

Ref Expression
Hypothesis rankid.1 A V
Assertion rankid A R1 suc rank A

Proof

Step Hyp Ref Expression
1 rankid.1 A V
2 unir1 R1 On = V
3 1 2 eleqtrri A R1 On
4 rankidb A R1 On A R1 suc rank A
5 3 4 ax-mp A R1 suc rank A