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Theorem add1p1 12464
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 11210 . . 3 (𝑁 ∈ ℂ → 1 ∈ ℂ)
31, 2, 2addassd 11237 . 2 (𝑁 ∈ ℂ → ((𝑁 + 1) + 1) = (𝑁 + (1 + 1)))
4 1p1e2 12338 . . . 4 (1 + 1) = 2
54a1i 11 . . 3 (𝑁 ∈ ℂ → (1 + 1) = 2)
65oveq2d 7420 . 2 (𝑁 ∈ ℂ → (𝑁 + (1 + 1)) = (𝑁 + 2))
73, 6eqtrd 2766 1 (𝑁 ∈ ℂ → ((𝑁 + 1) + 1) = (𝑁 + 2))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  wcel 2098  (class class class)co 7404  cc 11107  1c1 11110   + caddc 11112  2c2 12268
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697  ax-1cn 11167  ax-addass 11174
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-iota 6488  df-fv 6544  df-ov 7407  df-2 12276
This theorem is referenced by:  nneo  12647  ccatw2s1len  14579  chfacfscmul0  22711  chfacfscmulfsupp  22712  chfacfscmulgsum  22713  chfacfpmmul0  22715  chfacfpmmulfsupp  22716  chfacfpmmulgsum  22717  upgrwlkdvdelem  29498  poimirlem7  37006  fmtnoprmfac2  46788  fmtnofac1  46791  evenltle  46938
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