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Theorem syl5sseqr 3022
Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypotheses
Ref Expression
syl5sseqr.1 𝐵𝐴
syl5sseqr.2 (𝜑𝐶 = 𝐴)
Assertion
Ref Expression
syl5sseqr (𝜑𝐵𝐶)

Proof of Theorem syl5sseqr
StepHypRef Expression
1 syl5sseqr.1 . . 3 𝐵𝐴
21a1i 9 . 2 (𝜑𝐵𝐴)
3 syl5sseqr.2 . 2 (𝜑𝐶 = 𝐴)
42, 3sseqtr4d 3010 1 (𝜑𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1259  wss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959
This theorem is referenced by:  resdif  5176  fimacnv  5324  tfrlem5  5961
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