Metamath Proof Explorer


Theorem bnj1262

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

Ref Expression
Hypotheses bnj1262.1 ⊢ A ⊆ B
bnj1262.2 ⊢ φ → C = A
Assertion bnj1262 ⊢ φ → C ⊆ B

Proof

Step Hyp Ref Expression
1 bnj1262.1 ⊢ A ⊆ B
2 bnj1262.2 ⊢ φ → C = A
3 2 1 eqsstrdi ⊢ φ → C ⊆ B