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Metamath Proof Explorer

Theorem eldisjssd

Description: Subclass theorem for disjoint elementhood, deduction version. (Contributed by Peter Mazsa, 28-Sep-2021)

Ref Expression
Hypothesis eldisjssd.1 ⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
Assertion eldisjssd ( 𝜑 → ( ElDisj 𝐵 → ElDisj 𝐴 ) )

Proof

Step Hyp Ref Expression
1 eldisjssd.1 ⊢ ( 𝜑 → 𝐴 ⊆ 𝐵 )
2 eldisjss ⊢ ( 𝐴 ⊆ 𝐵 → ( ElDisj 𝐵 → ElDisj 𝐴 ) )
3 1 2 syl ⊢ ( 𝜑 → ( ElDisj 𝐵 → ElDisj 𝐴 ) )