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Metamath Proof Explorer

Theorem eqeq1

Description: Equality implies equivalence of equalities. (Contributed by NM, 26-May-1993) (Proof shortened by Wolf Lammen, 19-Nov-2019)

Ref Expression
Assertion eqeq1 
|- ( A = B -> ( A = C <-> B = C ) )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( A = B -> A = B )
2 1 eqeq1d 
 |-  ( A = B -> ( A = C <-> B = C ) )