Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > exnalim | GIF version |
Description: One direction of Theorem 19.14 of [Margaris] p. 90. In classical logic the converse also holds. (Contributed by Jim Kingdon, 15-Jul-2018.) |
Ref | Expression |
---|---|
exnalim | ⊢ (∃𝑥 ¬ 𝜑 → ¬ ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alexim 1632 | . 2 ⊢ (∀𝑥𝜑 → ¬ ∃𝑥 ¬ 𝜑) | |
2 | 1 | con2i 617 | 1 ⊢ (∃𝑥 ¬ 𝜑 → ¬ ∀𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1340 ∃wex 1479 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-17 1513 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 |
This theorem is referenced by: exanaliim 1634 alexnim 1635 nnal 1636 dtru 4531 brprcneu 5473 |
Copyright terms: Public domain | W3C validator |