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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 1509, but this proof does not use ax-17 1507.) (Contributed by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
nftru | ⊢ Ⅎ𝑥⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1336 | . 2 ⊢ ⊤ | |
2 | 1 | nfth 1441 | 1 ⊢ Ⅎ𝑥⊤ |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1333 Ⅎwnf 1437 |
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-gen 1426 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 |
This theorem is referenced by: nfmo 2020 dvelimc 2303 nfralxy 2474 nfrexxy 2475 nfralya 2476 nfrexya 2477 nfreuxy 2608 nfsbc 2933 nfcsb 3042 nfiotaw 5100 nfriota 5747 nfixpxy 6619 |
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