Theorem addcomi 8042

Description: Addition commutes. Based on ideas by Eric Schmidt. (Contributed by Scott Fenton, 3-Jan-2013.)

Hypotheses

Ref	Expression
mul.1	⊢ 𝐴 ∈ ℂ
mul.2	⊢ 𝐵 ∈ ℂ

Assertion

Ref	Expression
addcomi	⊢ (𝐴 + 𝐵) = (𝐵 + 𝐴)

Proof of Theorem addcomi

Step	Hyp	Ref	Expression
1		mul.1	. 2 ⊢ 𝐴 ∈ ℂ
2		mul.2	. 2 ⊢ 𝐵 ∈ ℂ
3		addcom 8035	. 2 ⊢ ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 + 𝐵) = (𝐵 + 𝐴))
4	1, 2, 3	mp2an 423	1 ⊢ (𝐴 + 𝐵) = (𝐵 + 𝐴)

Syntax hints:   = wceq 1343   ∈ wcel 2136  (class class class)co 5842  ℂcc 7751   + caddc 7756

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-addcom 7853

This theorem is referenced by:  addcomli  8043  add42i  8064  mvlladdi  8116  3m1e2  8977  fztpval  10018  fzo0to42pr  10155  ef01bndlem  11697  tangtx  13399  lgsdir2lem2  13570  lgsdir2lem3  13571  lgsdir2lem5  13573