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Theorem eqsstrrd 3165
 Description: Substitution of equality into a subclass relationship. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
eqsstrrd.1
eqsstrrd.2
Assertion
Ref Expression
eqsstrrd

Proof of Theorem eqsstrrd
StepHypRef Expression
1 eqsstrrd.1 . . 3
21eqcomd 2163 . 2
3 eqsstrrd.2 . 2
42, 3eqsstrd 3164 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1335   wss 3102 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-in 3108  df-ss 3115 This theorem is referenced by:  ssxpbm  5018  ssxp1  5019  ssxp2  5020  suppssof1  6043  tfrlemiubacc  6271  tfr1onlemubacc  6287  tfrcllemubacc  6300  oaword1  6411  phplem4dom  6800  fisseneq  6869  archnqq  7320  epttop  12450  metequiv2  12856  limccnpcntop  13004  limccnp2lem  13005  limccnp2cntop  13006  nnsf  13538
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