Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > peano2cn | GIF version |
Description: A theorem for complex numbers analogous the second Peano postulate peano2 4579. (Contributed by NM, 17-Aug-2005.) |
Ref | Expression |
---|---|
peano2cn | ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 7867 | . 2 ⊢ 1 ∈ ℂ | |
2 | addcl 7899 | . 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ) | |
3 | 1, 2 | mpan2 423 | 1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2141 (class class class)co 5853 ℂcc 7772 1c1 7775 + caddc 7777 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 107 ax-1cn 7867 ax-addcl 7870 |
This theorem is referenced by: xp1d2m1eqxm1d2 9130 nneo 9315 zeo 9317 zeo2 9318 zesq 10594 facndiv 10673 faclbnd 10675 faclbnd6 10678 bcxmas 11452 trireciplem 11463 odd2np1 11832 abssinper 13561 |
Copyright terms: Public domain | W3C validator |