| Mathbox for Wolf Lammen |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-nfsbtv | Structured version Visualization version GIF version | ||
| Description: Closed form of nfsbv 2330. (Contributed by Wolf Lammen, 2-May-2025.) |
| Ref | Expression |
|---|---|
| wl-nfsbtv | ⊢ (∀𝑥Ⅎ𝑧𝜑 → Ⅎ𝑧[𝑦 / 𝑥]𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | stdpc4 2068 | . 2 ⊢ (∀𝑥Ⅎ𝑧𝜑 → [𝑦 / 𝑥]Ⅎ𝑧𝜑) | |
| 2 | sbnf 2312 | . 2 ⊢ ([𝑦 / 𝑥]Ⅎ𝑧𝜑 ↔ Ⅎ𝑧[𝑦 / 𝑥]𝜑) | |
| 3 | 1, 2 | sylib 218 | 1 ⊢ (∀𝑥Ⅎ𝑧𝜑 → Ⅎ𝑧[𝑦 / 𝑥]𝜑) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∀wal 1538 Ⅎwnf 1783 [wsb 2064 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-10 2141 ax-11 2157 ax-12 2177 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-nf 1784 df-sb 2065 |
| This theorem is referenced by: wl-sb8eutv 37580 |
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