Description: Theorem *13.181 in WhiteheadRussell p. 178. (Contributed by Andrew Salmon, 3-Jun-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | pm13.181 | ⊢ ( ( 𝐴 = 𝐵 ∧ 𝐵 ≠ 𝐶 ) → 𝐴 ≠ 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom | ⊢ ( 𝐴 = 𝐵 ↔ 𝐵 = 𝐴 ) | |
2 | pm13.18 | ⊢ ( ( 𝐵 = 𝐴 ∧ 𝐵 ≠ 𝐶 ) → 𝐴 ≠ 𝐶 ) | |
3 | 1 2 | sylanb | ⊢ ( ( 𝐴 = 𝐵 ∧ 𝐵 ≠ 𝐶 ) → 𝐴 ≠ 𝐶 ) |