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Theorem sstrd 2949
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 2947 . 2 ((AB B𝐶) → A𝐶)
41, 2, 3syl2anc 391 1 (φA𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  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:  syl5ss  2950  syl6ss  2951  ssdif2d  3076  tfisi  4253  funss  4863  fssxp  5001  fvmptssdm  5198  suppssfv  5650  suppssov1  5651  tposss  5802  tfrlem1  5864  tfrlemibfn  5883  ecinxp  6117
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