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Theorem psstrd 3862
Description: Proper subclass inclusion is transitive. Deduction form of psstr 3859. (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 3859 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 565 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wpss 3722
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-ext 2750
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-ne 2943  df-in 3728  df-ss 3735  df-pss 3737
This theorem is referenced by: (None)
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