![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > nfdc | GIF version |
Description: If 𝑥 is not free in 𝜑, it is not free in DECID 𝜑. (Contributed by Jim Kingdon, 11-Mar-2018.) |
Ref | Expression |
---|---|
nfdc.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfdc | ⊢ Ⅎ𝑥DECID 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-dc 803 | . 2 ⊢ (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑)) | |
2 | nfdc.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | nfn 1619 | . . 3 ⊢ Ⅎ𝑥 ¬ 𝜑 |
4 | 2, 3 | nfor 1536 | . 2 ⊢ Ⅎ𝑥(𝜑 ∨ ¬ 𝜑) |
5 | 1, 4 | nfxfr 1433 | 1 ⊢ Ⅎ𝑥DECID 𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∨ wo 680 DECID wdc 802 Ⅎwnf 1419 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 586 ax-in2 587 ax-io 681 ax-5 1406 ax-gen 1408 ax-ie2 1453 ax-4 1470 ax-ial 1497 |
This theorem depends on definitions: df-bi 116 df-dc 803 df-tru 1317 df-fal 1320 df-nf 1420 |
This theorem is referenced by: 19.32dc 1640 finexdc 6749 ssfirab 6774 exfzdc 9910 nfsum1 11017 nfsum 11018 zsupcllemstep 11486 infssuzex 11490 ctiunctlemudc 11793 |
Copyright terms: Public domain | W3C validator |