Description: A transitive law for class equality. (Contributed by NM, 20-May-2005) (Proof shortened by Andrew Salmon, 25-May-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | eqtr2 | |- ( ( A = B /\ A = C ) -> B = C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom | |- ( A = B <-> B = A ) |
|
2 | eqtr | |- ( ( B = A /\ A = C ) -> B = C ) |
|
3 | 1 2 | sylanb | |- ( ( A = B /\ A = C ) -> B = C ) |