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Theorem add1p1 11633
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 10371 . . 3 (𝑁 ∈ ℂ → 1 ∈ ℂ)
31, 2, 2addassd 10399 . 2 (𝑁 ∈ ℂ → ((𝑁 + 1) + 1) = (𝑁 + (1 + 1)))
4 1p1e2 11507 . . . 4 (1 + 1) = 2
54a1i 11 . . 3 (𝑁 ∈ ℂ → (1 + 1) = 2)
65oveq2d 6938 . 2 (𝑁 ∈ ℂ → (𝑁 + (1 + 1)) = (𝑁 + 2))
73, 6eqtrd 2813 1 (𝑁 ∈ ℂ → ((𝑁 + 1) + 1) = (𝑁 + 2))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1601  wcel 2106  (class class class)co 6922  cc 10270  1c1 10273   + caddc 10275  2c2 11430
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-9 2115  ax-10 2134  ax-11 2149  ax-12 2162  ax-13 2333  ax-ext 2753  ax-1cn 10330  ax-addass 10337
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2763  df-cleq 2769  df-clel 2773  df-nfc 2920  df-rex 3095  df-rab 3098  df-v 3399  df-dif 3794  df-un 3796  df-in 3798  df-ss 3805  df-nul 4141  df-if 4307  df-sn 4398  df-pr 4400  df-op 4404  df-uni 4672  df-br 4887  df-iota 6099  df-fv 6143  df-ov 6925  df-2 11438
This theorem is referenced by:  nneo  11813  ccatw2s1len  13715  chfacfscmul0  21070  chfacfscmulfsupp  21071  chfacfscmulgsum  21072  chfacfpmmul0  21074  chfacfpmmulfsupp  21075  chfacfpmmulgsum  21076  upgrwlkdvdelem  27088  poimirlem7  34026  fmtnoprmfac2  42482  fmtnofac1  42485  evenltle  42633
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