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Theorem psstrd 4105
Description: Proper subclass inclusion is transitive. Deduction form of psstr 4102. (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 4102 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 583 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wpss 3948
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2938  df-v 3473  df-in 3954  df-ss 3964  df-pss 3966
This theorem is referenced by: (None)
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