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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