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Mirrors > Home > MPE Home > Th. List > nfsb2 | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for substitution. Usage of this theorem is discouraged because it depends on ax-13 2367. (Contributed by Mario Carneiro, 4-Oct-2016.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfsb2 | ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥[𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfna1 2142 | . 2 ⊢ Ⅎ𝑥 ¬ ∀𝑥 𝑥 = 𝑦 | |
2 | hbsb2 2477 | . 2 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)) | |
3 | 1, 2 | nf5d 2274 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥[𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1532 Ⅎwnf 1778 [wsb 2060 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-10 2130 ax-12 2167 ax-13 2367 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-ex 1775 df-nf 1779 df-sb 2061 |
This theorem is referenced by: nfsb4t 2494 sbco3 2508 sb9 2514 wl-nfs1t 37004 |
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