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Theorem syl6sseqr 3062
Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
syl6ssr.1 (𝜑𝐴𝐵)
syl6ssr.2 𝐶 = 𝐵
Assertion
Ref Expression
syl6sseqr (𝜑𝐴𝐶)

Proof of Theorem syl6sseqr
StepHypRef Expression
1 syl6ssr.1 . 2 (𝜑𝐴𝐵)
2 syl6ssr.2 . . 3 𝐶 = 𝐵
32eqcomi 2089 . 2 𝐵 = 𝐶
41, 3syl6sseq 3061 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287  wss 2988
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-in 2994  df-ss 3001
This theorem is referenced by:  iunpw  4274  iotanul  4958  iotass  4960  tfrlem9  6032  tfrlemibfn  6041  tfrlemiubacc  6043  tfrlemi14d  6046  tfr1onlemssrecs  6052  tfr1onlemres  6062  tfrcllemres  6075  exmidfodomrlemr  6765  exmidfodomrlemrALT  6766  uznnssnn  8990  shftfvalg  10141  shftfval  10144
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