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

Theorem eqsstrri 3189
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 19-Oct-1999.)
Hypotheses
Ref Expression
eqsstr3.1 𝐵 = 𝐴
eqsstr3.2 𝐵𝐶
Assertion
Ref Expression
eqsstrri 𝐴𝐶

Proof of Theorem eqsstrri
StepHypRef Expression
1 eqsstr3.1 . . 3 𝐵 = 𝐴
21eqcomi 2181 . 2 𝐴 = 𝐵
3 eqsstr3.2 . 2 𝐵𝐶
42, 3eqsstri 3188 1 𝐴𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1353  wss 3130
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 3136  df-ss 3143
This theorem is referenced by:  inss2  3357  dmv  4844  resasplitss  5396  ofrfval  6091  ofvalg  6092  ofrval  6093  off  6095  ofres  6097  ofco  6101  dftpos4  6264  smores2  6295  caseinj  7088  djuinj  7105  bcm1k  10740  bcpasc  10746
  Copyright terms: Public domain W3C validator