Theorem eqimss2 3293

Description: Equality implies the subclass relation. (Contributed by NM, 23-Nov-2003.)

Assertion

Ref	Expression
eqimss2	⊢ (𝐵 = 𝐴 → 𝐴 ⊆ 𝐵)

Proof of Theorem eqimss2

Step	Hyp	Ref	Expression
1		eqimss 3292	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 ⊆ 𝐵)
2	1	eqcoms 2235	1 ⊢ (𝐵 = 𝐴 → 𝐴 ⊆ 𝐵)

Syntax hints:   → wi 4   = wceq 1398   ⊆ wss 3211

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-in 3217  df-ss 3224

This theorem is referenced by:  ifpprsnssdc  3799  disjeq2  4089  disjeq1  4092  poeq2  4421  seeq1  4460  seeq2  4461  dmcoeq  5030  xp11m  5201  funeq  5372  fconst3m  5903  tposeq  6478  undifdcss  7183  nninfctlemfo  12736  ennnfonelemk  13151  ennnfonelemss  13161  qnnen  13182  imasaddfnlemg  13527  topgele  14894  topontopn  14902  txdis  15142  edgstruct  16059