![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > nftru | GIF version |
Description: The true constant has no free variables. (This can also be proven in one step with nfv 1538, but this proof does not use ax-17 1536.) (Contributed by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
nftru | ⊢ Ⅎ𝑥⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1367 | . 2 ⊢ ⊤ | |
2 | 1 | nfth 1474 | 1 ⊢ Ⅎ𝑥⊤ |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1364 Ⅎwnf 1470 |
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-gen 1459 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 |
This theorem is referenced by: nfmo 2057 dvelimc 2353 nfralw 2526 nfralxy 2527 nfrexxy 2528 nfralya 2529 nfrexya 2530 nfreuxy 2664 nfsbc 2997 nfcsbw 3107 nfcsb 3108 nfiotaw 5196 nfriota 5855 nfixpxy 6734 |
Copyright terms: Public domain | W3C validator |