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Theorem sspsstrd 3377
 Description: Transitivity involving subclass and proper subclass inclusion. Deduction form of sspsstr 3374. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
sspsstrd.1 (φA B)
sspsstrd.2 (φBC)
Assertion
Ref Expression
sspsstrd (φAC)

Proof of Theorem sspsstrd
StepHypRef Expression
1 sspsstrd.1 . 2 (φA B)
2 sspsstrd.2 . 2 (φBC)
3 sspsstr 3374 . 2 ((A B BC) → AC)
41, 2, 3syl2anc 642 1 (φAC)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊆ wss 3257   ⊊ wpss 3258 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pss 3261 This theorem is referenced by: (None)
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