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Theorem psssstrd 3942
 Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of psssstr 3939. (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 3939 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 581 1 (𝜑𝐴𝐶)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊆ wss 3798   ⊊ wpss 3799 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-ext 2803 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2812  df-cleq 2818  df-clel 2821  df-ne 3000  df-in 3805  df-ss 3812  df-pss 3814 This theorem is referenced by:  ackbij1lem15  9371  lsatssn0  35077  lsatexch  35118  lsatcvatlem  35124  lkrpssN  35238
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