MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  8p2e10OLD Structured version   Visualization version   GIF version

Theorem 8p2e10OLD 11126
Description: 8 + 2 = 10. (Contributed by NM, 5-Feb-2007.) Obsolete version of 8p2e10 11562 as of 8-Sep-2021. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
8p2e10OLD (8 + 2) = 10

Proof of Theorem 8p2e10OLD
StepHypRef Expression
1 df-2 11031 . . . . 5 2 = (1 + 1)
21oveq2i 6621 . . . 4 (8 + 2) = (8 + (1 + 1))
3 8cn 11058 . . . . 5 8 ∈ ℂ
4 ax-1cn 9946 . . . . 5 1 ∈ ℂ
53, 4, 4addassi 10000 . . . 4 ((8 + 1) + 1) = (8 + (1 + 1))
62, 5eqtr4i 2646 . . 3 (8 + 2) = ((8 + 1) + 1)
7 df-9 11038 . . . 4 9 = (8 + 1)
87oveq1i 6620 . . 3 (9 + 1) = ((8 + 1) + 1)
96, 8eqtr4i 2646 . 2 (8 + 2) = (9 + 1)
10 df-10OLD 11039 . 2 10 = (9 + 1)
119, 10eqtr4i 2646 1 (8 + 2) = 10
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  (class class class)co 6610  1c1 9889   + caddc 9891  2c2 11022  8c8 11028  9c9 11029  10c10 11030
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-resscn 9945  ax-1cn 9946  ax-icn 9947  ax-addcl 9948  ax-addrcl 9949  ax-mulcl 9950  ax-mulrcl 9951  ax-addass 9953  ax-i2m1 9956  ax-1ne0 9957  ax-rrecex 9960  ax-cnre 9961
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ne 2791  df-ral 2912  df-rex 2913  df-rab 2916  df-v 3191  df-dif 3562  df-un 3564  df-in 3566  df-ss 3573  df-nul 3897  df-if 4064  df-sn 4154  df-pr 4156  df-op 4160  df-uni 4408  df-br 4619  df-iota 5815  df-fv 5860  df-ov 6613  df-2 11031  df-3 11032  df-4 11033  df-5 11034  df-6 11035  df-7 11036  df-8 11037  df-9 11038  df-10OLD 11039
This theorem is referenced by:  8p2e10bOLD  11563  8p3e11OLD  11565  8t5e40OLD  11610
  Copyright terms: Public domain W3C validator