This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ra4v

Description: Version of ra4 with a disjoint variable condition, requiring fewer axioms. This is stdpc5v for a restricted domain. (Contributed by BJ, 27-Mar-2020)

Ref Expression
Assertion ra4v ⊢ ∀ x ∈ A φ → ψ → φ → ∀ x ∈ A ψ

Proof

Step Hyp Ref Expression
1 r19.21v ⊢ ∀ x ∈ A φ → ψ ↔ φ → ∀ x ∈ A ψ
2 1 biimpi ⊢ ∀ x ∈ A φ → ψ → φ → ∀ x ∈ A ψ