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Theorem syl5eqssr 2990
 Description: B chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
syl5eqssr.1 𝐵 = 𝐴
syl5eqssr.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
syl5eqssr (𝜑𝐴𝐶)

Proof of Theorem syl5eqssr
StepHypRef Expression
1 syl5eqssr.1 . . 3 𝐵 = 𝐴
21eqcomi 2044 . 2 𝐴 = 𝐵
3 syl5eqssr.2 . 2 (𝜑𝐵𝐶)
42, 3syl5eqss 2989 1 (𝜑𝐴𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1243   ⊆ wss 2917 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931 This theorem is referenced by:  relcnvtr  4840  resasplitss  5069  fimacnvdisj  5074  fimacnv  5296  f1ompt  5320
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