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Theorem exbidhOLD 1782
 Description: Obsolete proof of exbidh 1781 as of 16-Nov-2020. (Contributed by NM, 26-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
exbidh.1 (𝜑 → ∀𝑥𝜑)
exbidh.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
exbidhOLD (𝜑 → (∃𝑥𝜓 ↔ ∃𝑥𝜒))

Proof of Theorem exbidhOLD
StepHypRef Expression
1 exbidh.1 . . 3 (𝜑 → ∀𝑥𝜑)
2 exbidh.2 . . 3 (𝜑 → (𝜓𝜒))
31, 2alrimih 1741 . 2 (𝜑 → ∀𝑥(𝜓𝜒))
4 exbi 1762 . 2 (∀𝑥(𝜓𝜒) → (∃𝑥𝜓 ↔ ∃𝑥𝜒))
53, 4syl 17 1 (𝜑 → (∃𝑥𝜓 ↔ ∃𝑥𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195  ∀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-ex 1696 This theorem is referenced by: (None)
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