ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  4p4e8 GIF version

Theorem 4p4e8 8128
Description: 4 + 4 = 8. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
4p4e8 (4 + 4) = 8

Proof of Theorem 4p4e8
StepHypRef Expression
1 df-4 8051 . . . 4 4 = (3 + 1)
21oveq2i 5551 . . 3 (4 + 4) = (4 + (3 + 1))
3 4cn 8068 . . . 4 4 ∈ ℂ
4 3cn 8065 . . . 4 3 ∈ ℂ
5 ax-1cn 7035 . . . 4 1 ∈ ℂ
63, 4, 5addassi 7093 . . 3 ((4 + 3) + 1) = (4 + (3 + 1))
72, 6eqtr4i 2079 . 2 (4 + 4) = ((4 + 3) + 1)
8 df-8 8055 . . 3 8 = (7 + 1)
9 4p3e7 8127 . . . 4 (4 + 3) = 7
109oveq1i 5550 . . 3 ((4 + 3) + 1) = (7 + 1)
118, 10eqtr4i 2079 . 2 8 = ((4 + 3) + 1)
127, 11eqtr4i 2079 1 (4 + 4) = 8
Colors of variables: wff set class
Syntax hints:   = wceq 1259  (class class class)co 5540  1c1 6948   + caddc 6950  3c3 8041  4c4 8042  7c7 8045  8c8 8046
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-resscn 7034  ax-1cn 7035  ax-1re 7036  ax-addrcl 7039  ax-addass 7044
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-iota 4895  df-fv 4938  df-ov 5543  df-2 8049  df-3 8050  df-4 8051  df-5 8052  df-6 8053  df-7 8054  df-8 8055
This theorem is referenced by:  4t2e8  8141
  Copyright terms: Public domain W3C validator