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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 1473, but this proof does not use ax-17 1471.) (Contributed by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
nftru | ⊢ Ⅎ𝑥⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1300 | . 2 ⊢ ⊤ | |
2 | 1 | nfth 1405 | 1 ⊢ Ⅎ𝑥⊤ |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1297 Ⅎwnf 1401 |
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-gen 1390 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-nf 1402 |
This theorem is referenced by: nfmo 1975 dvelimc 2256 nfralxy 2425 nfrexxy 2426 nfralya 2427 nfrexya 2428 nfreuxy 2555 nfsbc 2874 nfcsb 2979 nfiotaxy 5018 nfriota 5655 nfixpxy 6514 |
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