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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 )