Theorem exlimiOLD 2209

Description: Obsolete proof of exlimi 2073 as of 6-Oct-2021. (Contributed by NM, 10-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
exlimiOLD.1	⊢ Ⅎ𝑥𝜓
exlimiOLD.2	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
exlimiOLD	⊢ (∃𝑥𝜑 → 𝜓)

Proof of Theorem exlimiOLD

Step	Hyp	Ref	Expression
1		exlimiOLD.1	. . 3 ⊢ Ⅎ𝑥𝜓
2	1	19.23OLD 2207	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓))
3		exlimiOLD.2	. 2 ⊢ (𝜑 → 𝜓)
4	2, 3	mpgbi 1716	1 ⊢ (∃𝑥𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1695  ℲwnfOLD 1700

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701  df-nfOLD 1712

This theorem is referenced by:  exlimihOLD  2210