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Theorem sspsstrd 4121
Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of sspsstr 4118. (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 4118 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴𝐶)
41, 2, 3syl2anc 584 1 (𝜑𝐴𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3963  wpss 3964
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1777  df-cleq 2727  df-ne 2939  df-ss 3980  df-pss 3983
This theorem is referenced by:  marypha1lem  9471  ackbij1lem15  10271  fin23lem38  10387  ltexprlem2  11075  mrieqv2d  17684
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