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Theorem syl6eqssr 2990
 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 2042 . 2 (φA = B)
3 syl6eqssr.2 . 2 B𝐶
42, 3syl6eqss 2989 1 (φA𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1242   ⊆ wss 2911 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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925 This theorem is referenced by:  ffvresb  5271  tposss  5802  iooval2  8534
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