ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  coeq12i Unicode version

Theorem coeq12i 4706
Description: Equality inference for composition of two classes. (Contributed by FL, 7-Jun-2012.)
Hypotheses
Ref Expression
coeq12i.1  |-  A  =  B
coeq12i.2  |-  C  =  D
Assertion
Ref Expression
coeq12i  |-  ( A  o.  C )  =  ( B  o.  D
)

Proof of Theorem coeq12i
StepHypRef Expression
1 coeq12i.1 . . 3  |-  A  =  B
21coeq1i 4702 . 2  |-  ( A  o.  C )  =  ( B  o.  C
)
3 coeq12i.2 . . 3  |-  C  =  D
43coeq2i 4703 . 2  |-  ( B  o.  C )  =  ( B  o.  D
)
52, 4eqtri 2161 1  |-  ( A  o.  C )  =  ( B  o.  D
)
Colors of variables: wff set class
Syntax hints:    = wceq 1332    o. ccom 4547
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-in 3078  df-ss 3085  df-br 3934  df-opab 3994  df-co 4552
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator