Metamath Proof Explorer


Theorem predeq3

Description: Equality theorem for the predecessor class. (Contributed by Scott Fenton, 2-Feb-2011)

Ref Expression
Assertion predeq3 X=YPredRAX=PredRAY

Proof

Step Hyp Ref Expression
1 eqid R=R
2 eqid A=A
3 predeq123 R=RA=AX=YPredRAX=PredRAY
4 1 2 3 mp3an12 X=YPredRAX=PredRAY