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Theorem syl6eqssr 3077
Description: A chained subclass and equality deduction. (Contributed by Mario Carneiro, 2-Jan-2017.)
Hypotheses
Ref Expression
syl6eqssr.1 (𝜑𝐵 = 𝐴)
syl6eqssr.2 𝐵𝐶
Assertion
Ref Expression
syl6eqssr (𝜑𝐴𝐶)

Proof of Theorem syl6eqssr
StepHypRef Expression
1 syl6eqssr.1 . . 3 (𝜑𝐵 = 𝐴)
21eqcomd 2093 . 2 (𝜑𝐴 = 𝐵)
3 syl6eqssr.2 . 2 𝐵𝐶
42, 3syl6eqss 3076 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1289  wss 2999
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 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3005  df-ss 3012
This theorem is referenced by:  ffvresb  5455  tposss  6003  sbthlemi5  6660  iooval2  9323  telfsumo  10847
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