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Mirrors > Home > NFE Home > Th. List > nftru | GIF version |
Description: The true constant has no free variables. (This can also be proven in one step with nfv 1619, but this proof does not use ax-17 1616.) (Contributed by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
nftru | ⊢ Ⅎx ⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1321 | . 2 ⊢ ⊤ | |
2 | 1 | nfth 1553 | 1 ⊢ Ⅎx ⊤ |
Colors of variables: wff setvar class |
Syntax hints: ⊤ wtru 1316 Ⅎwnf 1544 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 |
This theorem depends on definitions: df-bi 177 df-tru 1319 df-nf 1545 |
This theorem is referenced by: sbie 2038 nfeu 2220 nfmo 2221 dvelimc 2510 nfral 2667 nfreu 2785 nfrmo 2786 nfrab 2792 nfsbc 3067 nfcsb 3170 nfiota 4343 |
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