Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > nfi | Structured version Visualization version GIF version |
Description: Deduce that 𝑥 is not free in 𝜑 from the definition. (Contributed by Wolf Lammen, 15-Sep-2021.) |
Ref | Expression |
---|---|
nfi.1 | ⊢ (∃𝑥𝜑 → ∀𝑥𝜑) |
Ref | Expression |
---|---|
nfi | ⊢ Ⅎ𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfi.1 | . 2 ⊢ (∃𝑥𝜑 → ∀𝑥𝜑) | |
2 | df-nf 1791 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑)) | |
3 | 1, 2 | mpbir 234 | 1 ⊢ Ⅎ𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 ∃wex 1786 Ⅎwnf 1790 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 210 df-nf 1791 |
This theorem is referenced by: nfv 1921 nfcriOLD 2890 nfcriOLDOLD 2891 |
Copyright terms: Public domain | W3C validator |