Theorem exlimiOLD 2225

Description: Obsolete proof of exlimi 2089 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 2223	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓))
3		exlimiOLD.2	. 2 ⊢ (𝜑 → 𝜓)
4	2, 3	mpgbi 1722	1 ⊢ (∃𝑥𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1701  ℲwnfOLD 1706

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1841  ax-6 1890  ax-7 1937  ax-10 2021  ax-12 2049

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1702  df-nf 1707  df-nfOLD 1718

This theorem is referenced by:  exlimihOLD  2226