Metamath Proof Explorer


Theorem eqimssd

Description: Equality implies inclusion, deduction version. (Contributed by SN, 6-Nov-2024)

Ref Expression
Hypothesis eqimssd.1 ⊢ φ → A = B
Assertion eqimssd ⊢ φ → A ⊆ B

Proof

Step Hyp Ref Expression
1 eqimssd.1 ⊢ φ → A = B
2 ssid ⊢ B ⊆ B
3 1 2 eqsstrdi ⊢ φ → A ⊆ B