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Theorem sspsstrd 3677
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of sspsstr 3674. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
sspsstrd.1 (𝜑𝐴𝐵)
sspsstrd.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
sspsstrd (𝜑𝐴𝐶)

Proof of Theorem sspsstrd
StepHypRef Expression
1 sspsstrd.1 . 2 (𝜑𝐴𝐵)
2 sspsstrd.2 . 2 (𝜑𝐵𝐶)
3 sspsstr 3674 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 691 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3540  wpss 3541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-ne 2782  df-in 3547  df-ss 3554  df-pss 3556
This theorem is referenced by:  marypha1lem  8222  ackbij1lem15  8939  fin23lem38  9054  ltexprlem2  9738  mrieqv2d  16122
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