Theorem eqimss2i 3984

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 3945	. 2 ⊢ 𝐵 ⊆ 𝐵
2		eqimssi.1	. 2 ⊢ 𝐴 = 𝐵
3	1, 2	sseqtrri 3972	1 ⊢ 𝐵 ⊆ 𝐴

Syntax hints:   = wceq 1542   ⊆ wss 3890

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-cleq 2729  df-ss 3907

This theorem is referenced by:  cotr3  14934  supcvg  15815  prodfclim1  15852  ef0lem  16037  1strbas  17188  restid  17390  cayley  19383  gsumval3  19876  gsumzaddlem  19890  kgencn3  23536  hmeores  23749  opnfbas  23820  tsmsf1o  24123  ust0  24198  icchmeo  24921  plyeq0lem  26188  ulmdvlem1  26381  basellem7  27067  basellem9  27069  dchrisumlem3  27471  structvtxvallem  29106  struct2griedg  29114  gsumhashmul  33146  cycpmfvlem  33191  cycpmfv3  33194  constr01  33905  ivthALT  36536  aomclem4  43506  hashnzfzclim  44770  binomcxplemrat  44798  climsuselem1  46058  gsumfsupp  48673