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Metamath Proof Explorer

Theorem ssexd

Description: A subclass of a set is a set. Deduction form of ssexg . (Contributed by David Moews, 1-May-2017)

Ref Expression
Hypotheses ssexd.1 ⊢ ( 𝜑 → 𝐵 ∈ 𝐶 )
ssexd.2 ⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
Assertion ssexd ( 𝜑 → 𝐴 ∈ V )

Proof

Step Hyp Ref Expression
1 ssexd.1 ⊢ ( 𝜑 → 𝐵 ∈ 𝐶 )
2 ssexd.2 ⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
3 ssexg ⊢ ( ( 𝐴 ⊆ 𝐵 ∧ 𝐵 ∈ 𝐶 ) → 𝐴 ∈ V )
4 2 1 3 syl2anc ⊢ ( 𝜑 → 𝐴 ∈ V )