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Theorem bj-biexal2 36688
Description: When 𝜑 is substituted for 𝜓, both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-biexal2 (∀𝑥(∃𝑥𝜑𝜓) ↔ (∃𝑥𝜑 → ∀𝑥𝜓))

Proof of Theorem bj-biexal2
StepHypRef Expression
1 nfe1 2147 . 2 𝑥𝑥𝜑
2119.21 2204 1 (∀𝑥(∃𝑥𝜑𝜓) ↔ (∃𝑥𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  wal 1534  wex 1775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-10 2138  ax-12 2174
This theorem depends on definitions:  df-bi 207  df-ex 1776  df-nf 1780
This theorem is referenced by:  bj-biexal3  36689
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