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Mirrors > Home > MPE Home > Th. List > sb8fOLD | Structured version Visualization version GIF version |
Description: Obsolete version of sb8f 2343 as of 5-Dec-2024. (Contributed by NM, 16-May-1993.) (Revised by Wolf Lammen, 19-Jan-2023.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sb8f.nf | ⊢ Ⅎ𝑦𝜑 |
Ref | Expression |
---|---|
sb8fOLD | ⊢ (∀𝑥𝜑 ↔ ∀𝑦[𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb8f.nf | . 2 ⊢ Ⅎ𝑦𝜑 | |
2 | nfs1v 2145 | . 2 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 | |
3 | sbequ12 2235 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ [𝑦 / 𝑥]𝜑)) | |
4 | 1, 2, 3 | cbvalv1 2331 | 1 ⊢ (∀𝑥𝜑 ↔ ∀𝑦[𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∀wal 1531 Ⅎwnf 1777 [wsb 2059 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-10 2129 ax-11 2146 ax-12 2163 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-ex 1774 df-nf 1778 df-sb 2060 |
This theorem is referenced by: (None) |
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