Theorem eqimss2i 4044

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 4005	. 2 ⊢ 𝐵 ⊆ 𝐵
2		eqimssi.1	. 2 ⊢ 𝐴 = 𝐵
3	1, 2	sseqtrri 4020	1 ⊢ 𝐵 ⊆ 𝐴

Syntax hints:   = wceq 1542   ⊆ wss 3949

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3956  df-ss 3966

This theorem is referenced by:  cotr3  14925  supcvg  15802  prodfclim1  15839  ef0lem  16022  1strbas  17161  1strbasOLD  17162  restid  17379  cayley  19282  gsumval3  19775  gsumzaddlem  19789  kgencn3  23062  hmeores  23275  opnfbas  23346  tsmsf1o  23649  ust0  23724  icchmeo  24457  plyeq0lem  25724  ulmdvlem1  25912  basellem7  26591  basellem9  26593  dchrisumlem3  26994  structvtxvallem  28280  struct2griedg  28288  gsumhashmul  32208  cycpmfvlem  32271  cycpmfv3  32274  gg-icchmeo  35170  ivthALT  35220  aomclem4  41799  hashnzfzclim  43081  binomcxplemrat  43109  climsuselem1  44323  gsumfsupp  46592