Metamath Proof Explorer

Theorem r19.36vf

Description: Restricted quantifier version of one direction of 19.36 . (Contributed by Glauco Siliprandi, 23-Oct-2021)

Ref Expression
Hypothesis r19.36vf.1 x ψ
Assertion r19.36vf x A φ ψ x A φ ψ


Step Hyp Ref Expression
1 r19.36vf.1 x ψ
2 r19.35 x A φ ψ x A φ x A ψ
3 idd x A ψ ψ
4 1 3 rexlimi x A ψ ψ
5 4 imim2i x A φ x A ψ x A φ ψ
6 2 5 sylbi x A φ ψ x A φ ψ