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Theorem bj-biexex 33586
Description: A general FOL biconditional. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-biexex (∀𝑥(𝜑 → ∃𝑥𝜓) ↔ (∃𝑥𝜑 → ∃𝑥𝜓))

Proof of Theorem bj-biexex
StepHypRef Expression
1 nfe1 2088 . 2 𝑥𝑥𝜓
2119.23 2142 1 (∀𝑥(𝜑 → ∃𝑥𝜓) ↔ (∃𝑥𝜑 → ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  wal 1506  wex 1743
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  ax-7 1966  ax-10 2080  ax-12 2107
This theorem depends on definitions:  df-bi 199  df-ex 1744  df-nf 1748
This theorem is referenced by: (None)
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