Theorem 19.36imvOLD 1949

Description: Obsolete version of 19.36imv 1948 as of 22-Sep-2024. (Contributed by Rohan Ridenour, 16-Apr-2022.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.36imvOLD	⊢ (∃𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → 𝜓))

Distinct variable group:   𝜓,𝑥

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem 19.36imvOLD

Step	Hyp	Ref	Expression
1		19.35 1880	. . 3 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∃𝑥𝜓))
2	1	biimpi 215	. 2 ⊢ (∃𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → ∃𝑥𝜓))
3		ax5e 1915	. 2 ⊢ (∃𝑥𝜓 → 𝜓)
4	2, 3	syl6 35	1 ⊢ (∃𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → 𝜓))

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913

This theorem depends on definitions:  df-bi 206  df-ex 1783

This theorem is referenced by: (None)