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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfs1 | Structured version Visualization version GIF version | ||
| Description: Shorter proof of nfs1 2493 (three essential steps instead of four). (Contributed by BJ, 2-May-2019.) (Proof modification is discouraged.) |
| Ref | Expression |
|---|---|
| bj-nfs1.nf | ⊢ Ⅎ𝑦𝜑 |
| Ref | Expression |
|---|---|
| bj-nfs1 | ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bj-nfs1t2 36792 | . 2 ⊢ (∀𝑥Ⅎ𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑) | |
| 2 | bj-nfs1.nf | . 2 ⊢ Ⅎ𝑦𝜑 | |
| 3 | 1, 2 | mpg 1797 | 1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
| Colors of variables: wff setvar class |
| Syntax hints: 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-12 2177 ax-13 2377 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-ex 1780 df-nf 1784 df-sb 2065 |
| This theorem is referenced by: (None) |
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