Theorem eqimss2i 3885

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 3848	. 2 ⊢ 𝐵 ⊆ 𝐵
2		eqimssi.1	. 2 ⊢ 𝐴 = 𝐵
3	1, 2	sseqtr4i 3863	1 ⊢ 𝐵 ⊆ 𝐴

Syntax hints:   = wceq 1656   ⊆ wss 3798

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-ext 2803

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-in 3805  df-ss 3812

This theorem is referenced by:  cotr3  14103  supcvg  14969  prodfclim1  15005  ef0lem  15188  1strbas  16346  restid  16454  cayley  18191  gsumval3  18668  gsumzaddlem  18681  kgencn3  21739  hmeores  21952  opnfbas  22023  tsmsf1o  22325  ust0  22400  icchmeo  23117  plyeq0lem  24372  ulmdvlem1  24560  basellem7  25233  basellem9  25235  dchrisumlem3  25600  structvtxvallem  26325  struct2griedg  26333  ivthALT  32863  aomclem4  38469  hashnzfzclim  39360  binomcxplemrat  39388  climsuselem1  40632