Metamath Proof Explorer


Theorem infsdomnnOLD

Description: Obsolete version of infsdomnn as of 7-Jan-2025. (Contributed by NM, 22-Nov-2004) (Revised by Mario Carneiro, 27-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion infsdomnnOLD ω A B ω B A

Proof

Step Hyp Ref Expression
1 reldom Rel
2 1 brrelex1i ω A ω V
3 nnsdomg ω V B ω B ω
4 2 3 sylan ω A B ω B ω
5 simpl ω A B ω ω A
6 sdomdomtr B ω ω A B A
7 4 5 6 syl2anc ω A B ω B A