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Theorem sstrd 2955
 Description: Subclass transitivity deduction. (Contributed by NM, 2-Jun-2004.)
Hypotheses
Ref Expression
sstrd.1 (𝜑𝐴𝐵)
sstrd.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
sstrd (𝜑𝐴𝐶)

Proof of Theorem sstrd
StepHypRef Expression
1 sstrd.1 . 2 (𝜑𝐴𝐵)
2 sstrd.2 . 2 (𝜑𝐵𝐶)
3 sstr 2953 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 391 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:  syl5ss  2956  syl6ss  2957  ssdif2d  3082  tfisi  4310  funss  4920  fssxp  5058  fvmptssdm  5255  suppssfv  5708  suppssov1  5709  tposss  5861  tfrlem1  5923  tfrlemibfn  5942  ecinxp  6181
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