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Mirrors > Home > MPE Home > Th. List > nfd | Structured version Visualization version GIF version |
Description: Deduce that 𝑥 is not free in 𝜓 in a context. (Contributed by Wolf Lammen, 16-Sep-2021.) |
Ref | Expression |
---|---|
nfd.1 | ⊢ (𝜑 → (∃𝑥𝜓 → ∀𝑥𝜓)) |
Ref | Expression |
---|---|
nfd | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfd.1 | . 2 ⊢ (𝜑 → (∃𝑥𝜓 → ∀𝑥𝜓)) | |
2 | df-nf 1786 | . 2 ⊢ (Ⅎ𝑥𝜓 ↔ (∃𝑥𝜓 → ∀𝑥𝜓)) | |
3 | 1, 2 | sylibr 237 | 1 ⊢ (𝜑 → Ⅎ𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1536 ∃wex 1781 Ⅎwnf 1785 |
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 1786 |
This theorem is referenced by: nftht 1794 nfntht 1795 nfimd 1895 nf5-1 2146 axc16nf 2261 nfald 2336 nfeqf2 2384 bj-nfald 34552 |
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