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

Theorem 6p2e8 8837
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 8747 . . . . 5 2 = (1 + 1)
21oveq2i 5753 . . . 4 (6 + 2) = (6 + (1 + 1))
3 6cn 8770 . . . . 5 6 ∈ ℂ
4 ax-1cn 7681 . . . . 5 1 ∈ ℂ
53, 4, 4addassi 7742 . . . 4 ((6 + 1) + 1) = (6 + (1 + 1))
62, 5eqtr4i 2141 . . 3 (6 + 2) = ((6 + 1) + 1)
7 df-7 8752 . . . 4 7 = (6 + 1)
87oveq1i 5752 . . 3 (7 + 1) = ((6 + 1) + 1)
96, 8eqtr4i 2141 . 2 (6 + 2) = (7 + 1)
10 df-8 8753 . 2 8 = (7 + 1)
119, 10eqtr4i 2141 1 (6 + 2) = 8
Colors of variables: wff set class
Syntax hints:   = wceq 1316  (class class class)co 5742  1c1 7589   + caddc 7591  2c2 8739  6c6 8743  7c7 8744  8c8 8745
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-resscn 7680  ax-1cn 7681  ax-1re 7682  ax-addrcl 7685  ax-addass 7690
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-iota 5058  df-fv 5101  df-ov 5745  df-2 8747  df-3 8748  df-4 8749  df-5 8750  df-6 8751  df-7 8752  df-8 8753
This theorem is referenced by:  6p3e9  8838  6t3e18  9254
  Copyright terms: Public domain W3C validator