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Theorem sspsstrd 3047
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of sspsstr 3044. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
sspsstrd.1  C_
sspsstrd.2  C.  C
Assertion
Ref Expression
sspsstrd  C.  C

Proof of Theorem sspsstrd
StepHypRef Expression
1 sspsstrd.1 . 2  C_
2 sspsstrd.2 . 2  C.  C
3 sspsstr 3044 . 2  C_  C.  C  C.  C
41, 2, 3syl2anc 391 1  C.  C
Colors of variables: wff set class
Syntax hints:   wi 4    C_ wss 2911    C. wpss 2912
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-in1 544  ax-in2 545  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-ne 2203  df-in 2918  df-ss 2925  df-pss 2927
This theorem is referenced by: (None)
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