ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sseqtrdi GIF version

Theorem sseqtrdi 3146
Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
sseqtrdi.1 (𝜑𝐴𝐵)
sseqtrdi.2 𝐵 = 𝐶
Assertion
Ref Expression
sseqtrdi (𝜑𝐴𝐶)

Proof of Theorem sseqtrdi
StepHypRef Expression
1 sseqtrdi.1 . 2 (𝜑𝐴𝐵)
2 sseqtrdi.2 . . 3 𝐵 = 𝐶
32sseq2i 3125 . 2 (𝐴𝐵𝐴𝐶)
41, 3sylib 121 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1332  wss 3072
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 3078  df-ss 3085
This theorem is referenced by:  sseqtrrdi  3147  onintonm  4437  relrelss  5069  iotanul  5107  foimacnv  5389  cauappcvgprlemladdru  7484  zsumdc  11181  fsum3cvg3  11193  distop  12284  cnptoprest  12438  pwle2  13349  pw1nct  13354
  Copyright terms: Public domain W3C validator