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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfs1 | Structured version Visualization version GIF version |
Description: Shorter proof of nfs1 2491 (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 34659 | . 2 ⊢ (∀𝑥Ⅎ𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑) | |
2 | bj-nfs1.nf | . 2 ⊢ Ⅎ𝑦𝜑 | |
3 | 1, 2 | mpg 1805 | 1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1791 [wsb 2072 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2018 ax-10 2143 ax-12 2177 ax-13 2371 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-ex 1788 df-nf 1792 df-sb 2073 |
This theorem is referenced by: (None) |
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