Description: Equality theorem for the predecessor class. (Contributed by Scott Fenton, 2-Feb-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | predeq1 | |- ( R = S -> Pred ( R , A , X ) = Pred ( S , A , X ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- A = A |
|
2 | eqid | |- X = X |
|
3 | predeq123 | |- ( ( R = S /\ A = A /\ X = X ) -> Pred ( R , A , X ) = Pred ( S , A , X ) ) |
|
4 | 1 2 3 | mp3an23 | |- ( R = S -> Pred ( R , A , X ) = Pred ( S , A , X ) ) |