Description: Equality theorem for the predecessor class. (Contributed by Scott Fenton, 2-Feb-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | predeq3 | |- ( X = Y -> Pred ( R , A , X ) = Pred ( R , A , Y ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- R = R |
|
2 | eqid | |- A = A |
|
3 | predeq123 | |- ( ( R = R /\ A = A /\ X = Y ) -> Pred ( R , A , X ) = Pred ( R , A , Y ) ) |
|
4 | 1 2 3 | mp3an12 | |- ( X = Y -> Pred ( R , A , X ) = Pred ( R , A , Y ) ) |