New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  syl6sseqr Unicode version

Theorem syl6sseqr 3318
 Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
syl6ssr.1
syl6ssr.2
Assertion
Ref Expression
syl6sseqr

Proof of Theorem syl6sseqr
StepHypRef Expression
1 syl6ssr.1 . 2
2 syl6ssr.2 . . 3
32eqcomi 2357 . 2
41, 3syl6sseq 3317 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259 This theorem is referenced by:  ncssfin  6151  sbthlem1  6203
 Copyright terms: Public domain W3C validator