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Theorem syl6eqssr 2973
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 2027 . 2 (φA = B)
3 syl6eqssr.2 . 2 B𝐶
42, 3syl6eqss 2972 1 (φA𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1228  wss 2894
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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-in 2901  df-ss 2908
This theorem is referenced by:  ffvresb  5253  tposss  5783
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