Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  syl6sseqr GIF version

Theorem syl6sseqr 3096
 Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
syl6ssr.1 (𝜑𝐴𝐵)
syl6ssr.2 𝐶 = 𝐵
Assertion
Ref Expression
syl6sseqr (𝜑𝐴𝐶)

Proof of Theorem syl6sseqr
StepHypRef Expression
1 syl6ssr.1 . 2 (𝜑𝐴𝐵)
2 syl6ssr.2 . . 3 𝐶 = 𝐵
32eqcomi 2104 . 2 𝐵 = 𝐶
41, 3syl6sseq 3095 1 (𝜑𝐴𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1299   ⊆ wss 3021 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-11 1452  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082 This theorem depends on definitions:  df-bi 116  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-in 3027  df-ss 3034 This theorem is referenced by:  iunpw  4339  iotanul  5039  iotass  5041  tfrlem9  6146  tfrlemibfn  6155  tfrlemiubacc  6157  tfrlemi14d  6160  tfr1onlemssrecs  6166  tfr1onlemres  6176  tfrcllemres  6189  exmidfodomrlemr  6967  exmidfodomrlemrALT  6968  uznnssnn  9222  shftfvalg  10431  shftfval  10434  eltopss  11958  difopn  12059  tgrest  12120  txuni2  12206  tgioo  12465
 Copyright terms: Public domain W3C validator