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Mirrors > Home > MPE Home > Th. List > df-symdif | Structured version Visualization version GIF version |
Description: Define the symmetric difference of two classes. Alternate definitions are dfsymdif2 4251, dfsymdif3 4297 and dfsymdif4 4249. (Contributed by Scott Fenton, 31-Mar-2012.) |
Ref | Expression |
---|---|
df-symdif | ⊢ (𝐴 △ 𝐵) = ((𝐴 ∖ 𝐵) ∪ (𝐵 ∖ 𝐴)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cB | . . 3 class 𝐵 | |
3 | 1, 2 | csymdif 4242 | . 2 class (𝐴 △ 𝐵) |
4 | 1, 2 | cdif 3946 | . . 3 class (𝐴 ∖ 𝐵) |
5 | 2, 1 | cdif 3946 | . . 3 class (𝐵 ∖ 𝐴) |
6 | 4, 5 | cun 3947 | . 2 class ((𝐴 ∖ 𝐵) ∪ (𝐵 ∖ 𝐴)) |
7 | 3, 6 | wceq 1542 | 1 wff (𝐴 △ 𝐵) = ((𝐴 ∖ 𝐵) ∪ (𝐵 ∖ 𝐴)) |
Colors of variables: wff setvar class |
This definition is referenced by: symdifcom 4244 symdifeq1 4245 nfsymdif 4247 elsymdif 4248 difsssymdif 4253 dfsymdif3 4297 symdif0 5089 symdifv 5090 symdifid 5091 |
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