Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfs1t2 | Structured version Visualization version GIF version |
Description: A theorem close to a closed form of nfs1 2526. (Contributed by BJ, 2-May-2019.) |
Ref | Expression |
---|---|
bj-nfs1t2 | ⊢ (∀𝑥Ⅎ𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nf5r 2192 | . . 3 ⊢ (Ⅎ𝑦𝜑 → (𝜑 → ∀𝑦𝜑)) | |
2 | 1 | alimi 1811 | . 2 ⊢ (∀𝑥Ⅎ𝑦𝜑 → ∀𝑥(𝜑 → ∀𝑦𝜑)) |
3 | bj-nfs1t 34116 | . 2 ⊢ (∀𝑥(𝜑 → ∀𝑦𝜑) → Ⅎ𝑥[𝑦 / 𝑥]𝜑) | |
4 | 2, 3 | syl 17 | 1 ⊢ (∀𝑥Ⅎ𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1534 Ⅎwnf 1783 [wsb 2068 |
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 1969 ax-7 2014 ax-10 2144 ax-12 2176 ax-13 2389 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1780 df-nf 1784 df-sb 2069 |
This theorem is referenced by: bj-nfs1 34118 |
Copyright terms: Public domain | W3C validator |