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Theorem add1p1 12546
Description: Adding two times 1 to a number. (Contributed by AV, 22-Sep-2018.)
Assertion
Ref Expression
add1p1 (𝑁 ∈ ℂ → ((𝑁 + 1) + 1) = (𝑁 + 2))

Proof of Theorem add1p1
StepHypRef Expression
1 id 22 . . 3 (𝑁 ∈ ℂ → 𝑁 ∈ ℂ)
2 1cnd 11287 . . 3 (𝑁 ∈ ℂ → 1 ∈ ℂ)
31, 2, 2addassd 11314 . 2 (𝑁 ∈ ℂ → ((𝑁 + 1) + 1) = (𝑁 + (1 + 1)))
4 1p1e2 12420 . . . 4 (1 + 1) = 2
54a1i 11 . . 3 (𝑁 ∈ ℂ → (1 + 1) = 2)
65oveq2d 7466 . 2 (𝑁 ∈ ℂ → (𝑁 + (1 + 1)) = (𝑁 + 2))
73, 6eqtrd 2780 1 (𝑁 ∈ ℂ → ((𝑁 + 1) + 1) = (𝑁 + 2))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1537  wcel 2108  (class class class)co 7450  cc 11184  1c1 11187   + caddc 11189  2c2 12350
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-1cn 11244  ax-addass 11251
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5167  df-iota 6527  df-fv 6583  df-ov 7453  df-2 12358
This theorem is referenced by:  nneo  12729  ccatw2s1len  14675  chfacfscmul0  22887  chfacfscmulfsupp  22888  chfacfscmulgsum  22889  chfacfpmmul0  22891  chfacfpmmulfsupp  22892  chfacfpmmulgsum  22893  upgrwlkdvdelem  29774  poimirlem7  37589  fmtnoprmfac2  47443  fmtnofac1  47446  evenltle  47593
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