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Theorem psstrd 3998
Description: Proper subclass inclusion is transitive. Deduction form of psstr 3995. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
psstrd.1 (𝜑𝐴𝐵)
psstrd.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
psstrd (𝜑𝐴𝐶)

Proof of Theorem psstrd
StepHypRef Expression
1 psstrd.1 . 2 (𝜑𝐴𝐵)
2 psstrd.2 . 2 (𝜑𝐵𝐶)
3 psstr 3995 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 587 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wpss 3844
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-ne 2935  df-v 3400  df-in 3850  df-ss 3860  df-pss 3862
This theorem is referenced by: (None)
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