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Theorem syl5ss 2956
 Description: Subclass transitivity deduction. (Contributed by NM, 6-Feb-2014.)
Hypotheses
Ref Expression
syl5ss.1 𝐴𝐵
syl5ss.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
syl5ss (𝜑𝐴𝐶)

Proof of Theorem syl5ss
StepHypRef Expression
1 syl5ss.1 . . 3 𝐴𝐵
21a1i 9 . 2 (𝜑𝐴𝐵)
3 syl5ss.2 . 2 (𝜑𝐵𝐶)
42, 3sstrd 2955 1 (𝜑𝐴𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   ⊆ wss 2917 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931 This theorem is referenced by:  fimacnv  5296  smores2  5909  f1imaen2g  6273  phplem4dom  6324  genipv  6607  fzossnn0  9031
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