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Theorem sspsstrd 4016
 Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of sspsstr 4013. (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 4013 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 587 1 (𝜑𝐴𝐶)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊆ wss 3860   ⊊ wpss 3861 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 2113  ax-9 2121  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-ne 2952  df-v 3411  df-in 3867  df-ss 3877  df-pss 3879 This theorem is referenced by:  marypha1lem  8943  ackbij1lem15  9707  fin23lem38  9822  ltexprlem2  10510  mrieqv2d  16981
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