ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  deceq12i GIF version

Theorem deceq12i 8794
Description: Equality theorem for the decimal constructor. (Contributed by Mario Carneiro, 17-Apr-2015.)
Hypotheses
Ref Expression
deceq1i.1 𝐴 = 𝐵
deceq12i.2 𝐶 = 𝐷
Assertion
Ref Expression
deceq12i 𝐴𝐶 = 𝐵𝐷

Proof of Theorem deceq12i
StepHypRef Expression
1 deceq1i.1 . . 3 𝐴 = 𝐵
21deceq1i 8792 . 2 𝐴𝐶 = 𝐵𝐶
3 deceq12i.2 . . 3 𝐶 = 𝐷
43deceq2i 8793 . 2 𝐵𝐶 = 𝐵𝐷
52, 4eqtri 2105 1 𝐴𝐶 = 𝐵𝐷
Colors of variables: wff set class
Syntax hints:   = wceq 1287  cdc 8786
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-v 2616  df-un 2990  df-sn 3431  df-pr 3432  df-op 3434  df-uni 3631  df-br 3815  df-iota 4937  df-fv 4980  df-ov 5597  df-dec 8787
This theorem is referenced by:  11multnc  8853
  Copyright terms: Public domain W3C validator