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Theorem sstrid 3149
Description: Subclass transitivity deduction. (Contributed by NM, 6-Feb-2014.)
Hypotheses
Ref Expression
sstrid.1 𝐴𝐵
sstrid.2 (𝜑𝐵𝐶)
Assertion
Ref Expression
sstrid (𝜑𝐴𝐶)

Proof of Theorem sstrid
StepHypRef Expression
1 sstrid.1 . . 3 𝐴𝐵
21a1i 9 . 2 (𝜑𝐴𝐵)
3 sstrid.2 . 2 (𝜑𝐵𝐶)
42, 3sstrd 3148 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4  wss 3112
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 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-11 1493  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-in 3118  df-ss 3125
This theorem is referenced by:  cossxp2  5122  fimacnv  5609  smores2  6254  f1imaen2g  6751  phplem4dom  6820  isinfinf  6855  fidcenumlemrk  6911  casef  7045  genipv  7442  fzossnn0  10101  seq3split  10405  ctinf  12317  nninfdclemcl  12335  nninfdclemp1  12337  tgcl  12622  epttop  12648  ntrin  12682  cnconst2  12791  cnrest2  12794  cnptopresti  12796  cnptoprest2  12798  hmeores  12873  blin2  12990  ivthdec  13180  limcdifap  13189  limcresi  13193  dvfgg  13215  dvcnp2cntop  13221  dvaddxxbr  13223  reeff1olem  13250
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