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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(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑𝜓)))

Proof of Theorem exintrbiOLD
StepHypRef Expression
1 pm4.71 660 . . 3 ((𝜑𝜓) ↔ (𝜑 ↔ (𝜑𝜓)))
21albii 1737 . 2 (∀𝑥(𝜑𝜓) ↔ ∀𝑥(𝜑 ↔ (𝜑𝜓)))
3 exbi 1762 . 2 (∀𝑥(𝜑 ↔ (𝜑𝜓)) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑𝜓)))
42, 3sylbi 206 1 (∀𝑥(𝜑𝜓) → (∃𝑥𝜑 ↔ ∃𝑥(𝜑𝜓)))
 Colors of variables: wff setvar class 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)
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