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Metamath Proof Explorer

Theorem 1cosscnvepresex

Description: Sufficient condition for a restricted converse epsilon coset to be a set. (Contributed by Peter Mazsa, 24-Sep-2021)

Ref Expression
Assertion 1cosscnvepresex ⊢ A ∈ V → ≀ E -1 ↾ A ∈ V

Proof

Step Hyp Ref Expression
1 cnvepresex ⊢ A ∈ V → E -1 ↾ A ∈ V
2 cossex ⊢ E -1 ↾ A ∈ V → ≀ E -1 ↾ A ∈ V
3 1 2 syl ⊢ A ∈ V → ≀ E -1 ↾ A ∈ V