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Theorem syl6eqbrr 3830
 Description: A chained equality inference for a binary relation. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
syl6eqbrr.1 (𝜑𝐵 = 𝐴)
syl6eqbrr.2 𝐵𝑅𝐶
Assertion
Ref Expression
syl6eqbrr (𝜑𝐴𝑅𝐶)

Proof of Theorem syl6eqbrr
StepHypRef Expression
1 syl6eqbrr.1 . . 3 (𝜑𝐵 = 𝐴)
21eqcomd 2061 . 2 (𝜑𝐴 = 𝐵)
3 syl6eqbrr.2 . 2 𝐵𝑅𝐶
42, 3syl6eqbr 3829 1 (𝜑𝐴𝑅𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1259   class class class wbr 3792 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-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  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-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-br 3793 This theorem is referenced by: (None)
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