Mathbox for Wolf Lammen |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-cbv3vv | Structured version Visualization version GIF version |
Description: Avoiding ax-11 2021. (Contributed by Wolf Lammen, 30-Aug-2021.) |
Ref | Expression |
---|---|
wl-cbv3vv.nf | ⊢ Ⅎ𝑥𝜓 |
wl-cbv3vv.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
wl-cbv3vv | ⊢ (∀𝑥𝜑 → ∀𝑦𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-cbv3vv.nf | . . 3 ⊢ Ⅎ𝑥𝜓 | |
2 | wl-cbv3vv.1 | . . 3 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spimv1 2101 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) |
4 | 3 | alrimiv 1842 | 1 ⊢ (∀𝑥𝜑 → ∀𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 Ⅎwnf 1699 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nf 1701 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |