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Metamath Proof Explorer

Theorem eqsstrrid

Description: A chained subclass and equality deduction. (Contributed by NM, 25-Apr-2004)

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

Proof

Step Hyp Ref Expression
1 eqsstrrid.1 ⊢ B = A
2 eqsstrrid.2 ⊢ φ → B ⊆ C
3 1 eqcomi ⊢ A = B
4 3 2 eqsstrid ⊢ φ → A ⊆ C