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Theorem eqsstrrid 3175
Description: B chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
eqsstrrid.1 𝐵 = 𝐴
eqsstrrid.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
eqsstrrid (𝜑𝐴𝐶)

Proof of Theorem eqsstrrid
StepHypRef Expression
1 eqsstrrid.1 . . 3 𝐵 = 𝐴
21eqcomi 2161 . 2 𝐴 = 𝐵
3 eqsstrrid.2 . 2 (𝜑𝐵𝐶)
42, 3eqsstrid 3174 1 (𝜑𝐴𝐶)
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:  abnexg  4406  relcnvtr  5105  resasplitss  5349  fimacnvdisj  5354  fimacnv  5596  f1ompt  5618  tfr1onlemres  6296  tfrcllemres  6309
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