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Theorem syl6sseqr 3020
 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 2060 . 2 𝐵 = 𝐶
41, 3syl6sseq 3019 1 (𝜑𝐴𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1259   ⊆ wss 2945 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959 This theorem is referenced by:  iunpw  4239  iotanul  4910  iotass  4912  tfrlem9  5966  tfrlemibfn  5973  tfrlemiubacc  5975  tfrlemi14d  5978  uznnssnn  8616  shftfvalg  9647  shftfval  9650
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