Metamath Proof Explorer


Theorem eqimss2i

Description: Infer subclass relationship from equality. (Contributed by NM, 7-Jan-2007)

Ref Expression
Hypothesis eqimssi.1
|- A = B
Assertion eqimss2i
|- B C_ A

Proof

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