Metamath Proof Explorer


Theorem bnj1293

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypothesis bnj1293.1 ⊢ A = B ∩ C
Assertion bnj1293 ⊢ A ⊆ C

Proof

Step Hyp Ref Expression
1 bnj1293.1 ⊢ A = B ∩ C
2 inss2 ⊢ B ∩ C ⊆ C
3 1 2 eqsstri ⊢ A ⊆ C