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Theorem sstrd 2983
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 2981 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 397 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959
This theorem is referenced by:  syl5ss  2984  syl6ss  2985  ssdif2d  3110  tfisi  4338  funss  4948  fssxp  5086  fvmptssdm  5283  suppssfv  5736  suppssov1  5737  tposss  5892  tfrlem1  5954  tfrlemibfn  5973  ecinxp  6212
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