Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > exalim | GIF version |
Description: One direction of a classical definition of existential quantification. One direction of Definition of [Margaris] p. 49. For a decidable proposition, this is an equivalence, as seen as dfexdc 1390. (Contributed by Jim Kingdon, 29-Jul-2018.) |
Ref | Expression |
---|---|
exalim | ⊢ (∃𝑥𝜑 → ¬ ∀𝑥 ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alnex 1388 | . . 3 ⊢ (∀𝑥 ¬ 𝜑 ↔ ¬ ∃𝑥𝜑) | |
2 | 1 | biimpi 113 | . 2 ⊢ (∀𝑥 ¬ 𝜑 → ¬ ∃𝑥𝜑) |
3 | 2 | con2i 557 | 1 ⊢ (∃𝑥𝜑 → ¬ ∀𝑥 ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1241 ∃wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-5 1336 ax-gen 1338 ax-ie2 1383 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 |
This theorem is referenced by: n0rf 3233 ax9vsep 3880 |
Copyright terms: Public domain | W3C validator |