Metamath Proof Explorer


Theorem eqimssi

Description: Infer subclass relationship from equality. (Contributed by NM, 6-Jan-2007)

Ref Expression
Hypothesis eqimssi.1
|- A = B
Assertion eqimssi
|- A C_ B

Proof

Step Hyp Ref Expression
1 eqimssi.1
 |-  A = B
2 ssid
 |-  A C_ A
3 2 1 sseqtri
 |-  A C_ B