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Theorem sspsstrd 3857
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of sspsstr 3854. (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 3854 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 696 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3715  wpss 3716
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-ne 2933  df-in 3722  df-ss 3729  df-pss 3731
This theorem is referenced by:  marypha1lem  8506  ackbij1lem15  9268  fin23lem38  9383  ltexprlem2  10071  mrieqv2d  16521
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