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Theorem psssstrd 4061
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of psssstr 4058. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
psssstrd.1 (𝜑𝐴𝐵)
psssstrd.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
psssstrd (𝜑𝐴𝐶)

Proof of Theorem psssstrd
StepHypRef Expression
1 psssstrd.1 . 2 (𝜑𝐴𝐵)
2 psssstrd.2 . 2 (𝜑𝐵𝐶)
3 psssstr 4058 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 587 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3908  wpss 3909
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-ne 3012  df-v 3471  df-in 3915  df-ss 3925  df-pss 3927
This theorem is referenced by:  ackbij1lem15  9645  lsatssn0  36257  lsatexch  36298  lsatcvatlem  36304  lkrpssN  36418
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