Metamath Proof Explorer


Theorem rexlimiv

Description: Inference from Theorem 19.23 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994) Reduce dependencies on axioms. (Revised by Wolf Lammen, 14-Jan-2020)

Ref Expression
Hypothesis rexlimiv.1 ( 𝑥𝐴 → ( 𝜑𝜓 ) )
Assertion rexlimiv ( ∃ 𝑥𝐴 𝜑𝜓 )

Proof

Step Hyp Ref Expression
1 rexlimiv.1 ( 𝑥𝐴 → ( 𝜑𝜓 ) )
2 1 imp ( ( 𝑥𝐴𝜑 ) → 𝜓 )
3 2 rexlimiva ( ∃ 𝑥𝐴 𝜑𝜓 )