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Mirrors > Home > ILE Home > Th. List > addcomi | GIF version |
Description: Addition commutes. Based on ideas by Eric Schmidt. (Contributed by Scott Fenton, 3-Jan-2013.) |
Ref | Expression |
---|---|
mul.1 | ⊢ 𝐴 ∈ ℂ |
mul.2 | ⊢ 𝐵 ∈ ℂ |
Ref | Expression |
---|---|
addcomi | ⊢ (𝐴 + 𝐵) = (𝐵 + 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mul.1 | . 2 ⊢ 𝐴 ∈ ℂ | |
2 | mul.2 | . 2 ⊢ 𝐵 ∈ ℂ | |
3 | addcom 7892 | . 2 ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 + 𝐵) = (𝐵 + 𝐴)) | |
4 | 1, 2, 3 | mp2an 422 | 1 ⊢ (𝐴 + 𝐵) = (𝐵 + 𝐴) |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 ∈ wcel 1480 (class class class)co 5767 ℂcc 7611 + caddc 7616 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 107 ax-addcom 7713 |
This theorem is referenced by: addcomli 7900 add42i 7921 mvlladdi 7973 3m1e2 8833 fztpval 9856 fzo0to42pr 9990 ef01bndlem 11452 tangtx 12908 |
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