Metamath Proof Explorer


Theorem decaddi

Description: Add two numerals M and N (no carry). (Contributed by Mario Carneiro, 18-Feb-2014)

Ref Expression
Hypotheses decaddi.1 ⊢ A ∈ ℕ 0
decaddi.2 ⊢ B ∈ ℕ 0
decaddi.3 ⊢ N ∈ ℕ 0
decaddi.4 No typesetting found for |- M = ; A B with typecode |-
decaddi.5 ⊢ B + N = C
Assertion decaddi Could not format assertion : No typesetting found for |- ( M + N ) = ; A C with typecode |-

Proof

Step Hyp Ref Expression
1 decaddi.1 ⊢ A ∈ ℕ 0
2 decaddi.2 ⊢ B ∈ ℕ 0
3 decaddi.3 ⊢ N ∈ ℕ 0
4 decaddi.4 Could not format M = ; A B : No typesetting found for |- M = ; A B with typecode |-
5 decaddi.5 ⊢ B + N = C
6 0nn0 ⊢ 0 ∈ ℕ 0
7 3 dec0h ⊢ N = 0N
8 1 nn0cni ⊢ A ∈ ℂ
9 8 addridi ⊢ A + 0 = A
10 1 2 6 3 4 7 9 5 decadd Could not format ( M + N ) = ; A C : No typesetting found for |- ( M + N ) = ; A C with typecode |-