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Theorem exnalimn 1844
Description: Existential quantification of a conjunction expressed with only primitive symbols (, ¬, ). (Contributed by NM, 10-May-1993.) State the most general instance. (Revised by BJ, 29-Sep-2019.)
Assertion
Ref Expression
exnalimn (∃𝑥(𝜑𝜓) ↔ ¬ ∀𝑥(𝜑 → ¬ 𝜓))

Proof of Theorem exnalimn
StepHypRef Expression
1 alinexa 1843 . 2 (∀𝑥(𝜑 → ¬ 𝜓) ↔ ¬ ∃𝑥(𝜑𝜓))
21con2bii 360 1 (∃𝑥(𝜑𝜓) ↔ ¬ ∀𝑥(𝜑 → ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 208  wa 398  wal 1535  wex 1780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781
This theorem is referenced by:  r2exlem  3287  wl-dfrexf  34884  wl-dfrexv  34886
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