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Metamath Proof Explorer

Theorem sstrdi

Description: Subclass transitivity deduction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

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

Proof

Step Hyp Ref Expression
1 sstrdi.1 ⊢ φ → A ⊆ B
2 sstrdi.2 ⊢ B ⊆ C
3 2 a1i ⊢ φ → B ⊆ C
4 1 3 sstrd ⊢ φ → A ⊆ C