Theorem rexlimivwOLD 3180

Description: Obsolete version of rexlimivw 3145 as of 23-Dec-2024. (Contributed by FL, 19-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
rexlimivwOLD.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
rexlimivwOLD	⊢ (∃𝑥 ∈ 𝐴 𝜑 → 𝜓)

Distinct variable group:   𝜓,𝑥

Allowed substitution hints:   𝜑(𝑥)   𝐴(𝑥)

Proof of Theorem rexlimivwOLD

Step	Hyp	Ref	Expression
1		rexlimivwOLD.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	a1i 11	. 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 → 𝜓))
3	2	rexlimiv 3142	1 ⊢ (∃𝑥 ∈ 𝐴 𝜑 → 𝜓)

Syntax hints:   → wi 4   ∈ wcel 2104  ∃wrex 3071

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911

This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1780  df-rex 3072

This theorem is referenced by: (None)