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 )