Description: Equality deduction for class intersection. (Contributed by NM, 2-Sep-2003)
Ref | Expression | ||
---|---|---|---|
Hypothesis | inteqd.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
Assertion | inteqd | ⊢ ( 𝜑 → ∩ 𝐴 = ∩ 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inteqd.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | inteq | ⊢ ( 𝐴 = 𝐵 → ∩ 𝐴 = ∩ 𝐵 ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ∩ 𝐴 = ∩ 𝐵 ) |