Description: A member of an unordered pair of classes is one or the other of them. Exercise 1 of TakeutiZaring p. 15. (Contributed by NM, 13-Sep-1995)
Ref | Expression | ||
---|---|---|---|
Hypothesis | elpr.1 | ⊢ 𝐴 ∈ V | |
Assertion | elpr | ⊢ ( 𝐴 ∈ { 𝐵 , 𝐶 } ↔ ( 𝐴 = 𝐵 ∨ 𝐴 = 𝐶 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elpr.1 | ⊢ 𝐴 ∈ V | |
2 | elprg | ⊢ ( 𝐴 ∈ V → ( 𝐴 ∈ { 𝐵 , 𝐶 } ↔ ( 𝐴 = 𝐵 ∨ 𝐴 = 𝐶 ) ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐴 ∈ { 𝐵 , 𝐶 } ↔ ( 𝐴 = 𝐵 ∨ 𝐴 = 𝐶 ) ) |