Theorem eqimss2i 3282

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

Hypothesis

Ref	Expression
eqimssi.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
eqimss2i	⊢ 𝐵 ⊆ 𝐴

Proof of Theorem eqimss2i

Step	Hyp	Ref	Expression
1		ssid 3245	. 2 ⊢ 𝐵 ⊆ 𝐵
2		eqimssi.1	. 2 ⊢ 𝐴 = 𝐵
3	1, 2	sseqtrri 3260	1 ⊢ 𝐵 ⊆ 𝐴

Syntax hints:   = wceq 1395   ⊆ wss 3198

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3204  df-ss 3211

This theorem is referenced by:  cocnvres  5259  cocnvss  5260  fsum3  11938  prodfclim1  12095  ef0lem  12211  restid  13323  hmeores  15029  struct2slots2dom  15879  struct2griedg  15887