Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | bnj1322 | ⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∩ 𝐵 ) = 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss | ⊢ ( 𝐴 = 𝐵 → 𝐴 ⊆ 𝐵 ) | |
2 | df-ss | ⊢ ( 𝐴 ⊆ 𝐵 ↔ ( 𝐴 ∩ 𝐵 ) = 𝐴 ) | |
3 | 1 2 | sylib | ⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∩ 𝐵 ) = 𝐴 ) |