ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  6p2e8 Structured version   GIF version

Theorem 6p2e8 7799
Description: 6 + 2 = 8. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
6p2e8 (6 + 2) = 8

Proof of Theorem 6p2e8
StepHypRef Expression
1 df-2 7713 . . . . 5 2 = (1 + 1)
21oveq2i 5466 . . . 4 (6 + 2) = (6 + (1 + 1))
3 6cn 7737 . . . . 5 6
4 ax-1cn 6736 . . . . 5 1
53, 4, 4addassi 6793 . . . 4 ((6 + 1) + 1) = (6 + (1 + 1))
62, 5eqtr4i 2060 . . 3 (6 + 2) = ((6 + 1) + 1)
7 df-7 7718 . . . 4 7 = (6 + 1)
87oveq1i 5465 . . 3 (7 + 1) = ((6 + 1) + 1)
96, 8eqtr4i 2060 . 2 (6 + 2) = (7 + 1)
10 df-8 7719 . 2 8 = (7 + 1)
119, 10eqtr4i 2060 1 (6 + 2) = 8
Colors of variables: wff set class
Syntax hints:   = wceq 1242  (class class class)co 5455  1c1 6672   + caddc 6674  2c2 7704  6c6 7708  7c7 7709  8c8 7710
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-resscn 6735  ax-1cn 6736  ax-1re 6737  ax-addrcl 6740  ax-addass 6745
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458  df-2 7713  df-3 7714  df-4 7715  df-5 7716  df-6 7717  df-7 7718  df-8 7719
This theorem is referenced by:  6p3e9  7800  6t3e18  8181
  Copyright terms: Public domain W3C validator