Description: Equality relationship among four classes. (Contributed by NM, 3-Aug-1994)
Ref | Expression | ||
---|---|---|---|
Assertion | eqeq12 | ⊢ ( ( 𝐴 = 𝐵 ∧ 𝐶 = 𝐷 ) → ( 𝐴 = 𝐶 ↔ 𝐵 = 𝐷 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 | ⊢ ( 𝐴 = 𝐵 → ( 𝐴 = 𝐶 ↔ 𝐵 = 𝐶 ) ) | |
2 | eqeq2 | ⊢ ( 𝐶 = 𝐷 → ( 𝐵 = 𝐶 ↔ 𝐵 = 𝐷 ) ) | |
3 | 1 2 | sylan9bb | ⊢ ( ( 𝐴 = 𝐵 ∧ 𝐶 = 𝐷 ) → ( 𝐴 = 𝐶 ↔ 𝐵 = 𝐷 ) ) |