Theorem reximiaOLD 3177

Description: Obsolete version of reximia 3176 as of 31-Oct-2024. (Contributed by NM, 10-Feb-1997.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
reximia.1	⊢ (𝑥 ∈ 𝐴 → (𝜑 → 𝜓))

Assertion

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

Proof of Theorem reximiaOLD

Step	Hyp	Ref	Expression
1		rexim 3172	. 2 ⊢ (∀𝑥 ∈ 𝐴 (𝜑 → 𝜓) → (∃𝑥 ∈ 𝐴 𝜑 → ∃𝑥 ∈ 𝐴 𝜓))
2		reximia.1	. 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 → 𝜓))
3	1, 2	mprg 3078	1 ⊢ (∃𝑥 ∈ 𝐴 𝜑 → ∃𝑥 ∈ 𝐴 𝜓)

Syntax hints:   → wi 4   ∈ wcel 2106  ∃wrex 3065

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783  df-ral 3069  df-rex 3070

This theorem is referenced by: (None)