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Theorem psssstrd 4083
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of psssstr 4080. (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 4080 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 584 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3933  wpss 3934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-ne 3014  df-in 3940  df-ss 3949  df-pss 3951
This theorem is referenced by:  ackbij1lem15  9644  lsatssn0  36018  lsatexch  36059  lsatcvatlem  36065  lkrpssN  36179
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