![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > hbn | GIF version |
Description: If 𝑥 is not free in 𝜑, it is not free in ¬ 𝜑. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
hbn.1 | ⊢ (𝜑 → ∀𝑥𝜑) |
Ref | Expression |
---|---|
hbn | ⊢ (¬ 𝜑 → ∀𝑥 ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbnt 1653 | . 2 ⊢ (∀𝑥(𝜑 → ∀𝑥𝜑) → (¬ 𝜑 → ∀𝑥 ¬ 𝜑)) | |
2 | hbn.1 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
3 | 1, 2 | mpg 1451 | 1 ⊢ (¬ 𝜑 → ∀𝑥 ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1351 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-5 1447 ax-gen 1449 ax-ie2 1494 ax-4 1510 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 |
This theorem is referenced by: hbnae 1721 sbn 1952 euor 2052 euor2 2084 |
Copyright terms: Public domain | W3C validator |