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Theorem syl5ss 3284
Description: Subclass transitivity deduction. (Contributed by NM, 6-Feb-2014.)
Hypotheses
Ref Expression
syl5ss.1 A B
syl5ss.2 (φB C)
Assertion
Ref Expression
syl5ss (φA C)

Proof of Theorem syl5ss
StepHypRef Expression
1 syl5ss.1 . . 3 A B
21a1i 10 . 2 (φA B)
3 syl5ss.2 . 2 (φB C)
42, 3sstrd 3283 1 (φA C)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wss 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 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-ss 3260
This theorem is referenced by:  fssxp  5233  fimacnv  5412  fvmptss  5706  enprmaplem6  6082  sbthlem1  6204
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