Theorem exmoOLD 2620

Description: Obsolete proof of exmo 2551 as of 31-Dec-2022. (Contributed by NM, 8-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
exmoOLD	⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Proof of Theorem exmoOLD

Step	Hyp	Ref	Expression
1		pm2.21 121	. . 3 ⊢ (¬ ∃𝑥𝜑 → (∃𝑥𝜑 → ∃!𝑥𝜑))
2		moeu 2603	. . 3 ⊢ (∃*𝑥𝜑 ↔ (∃𝑥𝜑 → ∃!𝑥𝜑))
3	1, 2	sylibr 226	. 2 ⊢ (¬ ∃𝑥𝜑 → ∃*𝑥𝜑)
4	3	orri 849	1 ⊢ (∃𝑥𝜑 ∨ ∃*𝑥𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 834  ∃wex 1743  ∃*wmo 2546  ∃!weu 2584

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1759  ax-4 1773  ax-5 1870  ax-6 1929

This theorem depends on definitions:  df-bi 199  df-an 388  df-or 835  df-ex 1744  df-mo 2548  df-eu 2585

This theorem is referenced by: (None)