Theorem exintrbiOLD 1809

Description: Obsolete proof of exintrbi 1808 as of 16-Nov-2020. (Contributed by Raph Levien, 3-Jul-2006.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
exintrbiOLD	⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑 ∧ 𝜓)))

Proof of Theorem exintrbiOLD

Step	Hyp	Ref	Expression
1		pm4.71 660	. . 3 ⊢ ((𝜑 → 𝜓) ↔ (𝜑 ↔ (𝜑 ∧ 𝜓)))
2	1	albii 1737	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) ↔ ∀𝑥(𝜑 ↔ (𝜑 ∧ 𝜓)))
3		exbi 1762	. 2 ⊢ (∀𝑥(𝜑 ↔ (𝜑 ∧ 𝜓)) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑 ∧ 𝜓)))
4	2, 3	sylbi 206	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑 ∧ 𝜓)))

Syntax hints:   → wi 4   ↔ wb 195   ∧ wa 383  ∀wal 1473  ∃wex 1695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696

This theorem is referenced by: (None)