Metamath Proof Explorer


Theorem sswf

Description: A subset of a well-founded set is well-founded. (Contributed by Mario Carneiro, 17-Nov-2014)

Ref Expression
Assertion sswf AR1OnBABR1On

Proof

Step Hyp Ref Expression
1 rankidb AR1OnAR1sucrankA
2 r1sscl AR1sucrankABABR1sucrankA
3 1 2 sylan AR1OnBABR1sucrankA
4 r1elwf BR1sucrankABR1On
5 3 4 syl AR1OnBABR1On