ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sseq1i GIF version

Theorem sseq1i 3181
Description: An equality inference for the subclass relationship. (Contributed by NM, 18-Aug-1993.)
Hypothesis
Ref Expression
sseq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
sseq1i (𝐴𝐶𝐵𝐶)

Proof of Theorem sseq1i
StepHypRef Expression
1 sseq1i.1 . 2 𝐴 = 𝐵
2 sseq1 3178 . 2 (𝐴 = 𝐵 → (𝐴𝐶𝐵𝐶))
31, 2ax-mp 5 1 (𝐴𝐶𝐵𝐶)
Colors of variables: wff set class
Syntax hints:  wb 105   = 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:  eqsstri  3187  eqsstrid  3201  ssab  3225  rabss  3232  uniiunlem  3244  prss  3747  prssg  3748  tpss  3756  iunss  3925  pwtr  4216  ordsucss  4500  elomssom  4601  cores2  5137  dffun2  5222  funimaexglem  5295  idref  5752  ordgt0ge1  6430  3nsssucpw1  7229  prarloclemn  7489  bdeqsuc  14289  bj-omssind  14343
  Copyright terms: Public domain W3C validator