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Theorem psssstrd 3694
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of psssstr 3691. (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 3691 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 692 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3555  wpss 3556
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-ne 2791  df-in 3562  df-ss 3569  df-pss 3571
This theorem is referenced by:  ackbij1lem15  9000  lsatssn0  33769  lsatexch  33810  lsatcvatlem  33816  lkrpssN  33930
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