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Theorem sseqtrrid 3154
 Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
sseqtrrid.1 𝐵𝐴
sseqtrrid.2 (𝜑𝐶 = 𝐴)
Assertion
Ref Expression
sseqtrrid (𝜑𝐵𝐶)

Proof of Theorem sseqtrrid
StepHypRef Expression
1 sseqtrrid.1 . . 3 𝐵𝐴
21a1i 9 . 2 (𝜑𝐵𝐴)
3 sseqtrrid.2 . 2 (𝜑𝐶 = 𝐴)
42, 3sseqtrrd 3142 1 (𝜑𝐵𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1332   ⊆ wss 3077 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3083  df-ss 3090 This theorem is referenced by:  resdif  5398  fimacnv  5558  tfrlem5  6220  fsumsplit  11228  phimullem  11957  ennnfonelemss  11979  istopon  12239  sscls  12348  mopnfss  12675
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