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

Theorem sseqtrrdi 3204
Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004.)
Hypotheses
Ref Expression
sseqtrrdi.1 (𝜑𝐴𝐵)
sseqtrrdi.2 𝐶 = 𝐵
Assertion
Ref Expression
sseqtrrdi (𝜑𝐴𝐶)

Proof of Theorem sseqtrrdi
StepHypRef Expression
1 sseqtrrdi.1 . 2 (𝜑𝐴𝐵)
2 sseqtrrdi.2 . . 3 𝐶 = 𝐵
32eqcomi 2181 . 2 𝐵 = 𝐶
41, 3sseqtrdi 3203 1 (𝜑𝐴𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  wss 3129
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142
This theorem is referenced by:  iunpw  4476  iotanul  5188  iotass  5190  tfrlem9  6313  tfrlemibfn  6322  tfrlemiubacc  6324  tfrlemi14d  6327  tfr1onlemssrecs  6333  tfr1onlemres  6343  tfrcllemres  6356  exmidfodomrlemr  7194  exmidfodomrlemrALT  7195  uznnssnn  9553  shftfvalg  10798  shftfval  10801  clim2prod  11518  reldvdsrsrg  13073  dvdsrvald  13074  dvdsrex  13079  eltopss  13140  difopn  13241  tgrest  13302  txuni2  13389  tgioo  13679
  Copyright terms: Public domain W3C validator