Description: Infer subclass relationship from equality. (Contributed by NM, 7-Jan-2007)
Ref | Expression | ||
---|---|---|---|
Hypothesis | eqimssi.1 | $${\u22a2}{A}={B}$$ | |
Assertion | eqimss2i | $${\u22a2}{B}\subseteq {A}$$ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimssi.1 | $${\u22a2}{A}={B}$$ | |
2 | ssid | $${\u22a2}{B}\subseteq {B}$$ | |
3 | 2 1 | sseqtrri | $${\u22a2}{B}\subseteq {A}$$ |