Theorem eqimss2i 3000

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

Hypothesis

Ref	Expression
eqimssi.1	|- A = B

Assertion

Ref	Expression
eqimss2i	|- B C_ A

Proof of Theorem eqimss2i

Step	Hyp	Ref	Expression
1		ssid 2964	. 2 |- B C_ B
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtr4i 2978	1 |- B C_ A

Syntax hints:   = wceq 1243   C_ wss 2917

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931

This theorem is referenced by: (None)