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Metamath Proof Explorer

Theorem eqsstrdi

Description: A chained subclass and equality deduction. (Contributed by Mario Carneiro, 2-Jan-2017)

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

Proof

Step Hyp Ref Expression
1 eqsstrdi.1 ⊢ φ → A = B
2 eqsstrdi.2 ⊢ B ⊆ C
3 2 a1i ⊢ φ → B ⊆ C
4 1 3 eqsstrd ⊢ φ → A ⊆ C