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Mirrors > Home > ILE Home > Th. List > peano2cn | GIF version |
Description: A theorem for complex numbers analogous the second Peano postulate peano2 4566. (Contributed by NM, 17-Aug-2005.) |
Ref | Expression |
---|---|
peano2cn | ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 7837 | . 2 ⊢ 1 ∈ ℂ | |
2 | addcl 7869 | . 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ) | |
3 | 1, 2 | mpan2 422 | 1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2135 (class class class)co 5836 ℂcc 7742 1c1 7745 + caddc 7747 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 107 ax-1cn 7837 ax-addcl 7840 |
This theorem is referenced by: xp1d2m1eqxm1d2 9100 nneo 9285 zeo 9287 zeo2 9288 zesq 10562 facndiv 10641 faclbnd 10643 faclbnd6 10646 bcxmas 11416 trireciplem 11427 odd2np1 11795 abssinper 13308 |
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