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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 2363. (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 2141 | . 2 ⊢ Ⅎ𝑥 ¬ ∀𝑥 𝑥 = 𝑦 | |
2 | hbsb2 2473 | . 2 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)) | |
3 | 1, 2 | nf5d 2272 | 1 ⊢ (¬ ∀𝑥 𝑥 = 𝑦 → Ⅎ𝑥[𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀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-12 2163 ax-13 2363 |
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: nfsb4t 2490 sbco3 2504 sb9 2510 wl-nfs1t 36906 |
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