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Metamath Proof Explorer

Theorem rexlimivw

Description: Weaker version of rexlimiv . (Contributed by FL, 19-Sep-2011) (Proof shortened by Wolf Lammen, 23-Dec-2024)

Ref Expression
Hypothesis rexlimivw.1 ⊢ ( 𝜑 → 𝜓 )
Assertion rexlimivw ( ∃ 𝑥 ∈ 𝐴 𝜑 → 𝜓 )

Proof

Step Hyp Ref Expression
1 rexlimivw.1 ⊢ ( 𝜑 → 𝜓 )
2 1 adantl ⊢ ( ( 𝑥 ∈ 𝐴 ∧ 𝜑 ) → 𝜓 )
3 2 rexlimiva ⊢ ( ∃ 𝑥 ∈ 𝐴 𝜑 → 𝜓 )