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Theorem sspsstrd 4069
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of sspsstr 4066. (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 4066 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 585 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3911  wpss 3912
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ne 2941  df-v 3446  df-in 3918  df-ss 3928  df-pss 3930
This theorem is referenced by:  marypha1lem  9374  ackbij1lem15  10175  fin23lem38  10290  ltexprlem2  10978  mrieqv2d  17524
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