Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nfra2xy | GIF version |
Description: Not-free given two restricted quantifiers. (Contributed by Jim Kingdon, 20-Aug-2018.) |
Ref | Expression |
---|---|
nfra2xy | ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2258 | . 2 ⊢ Ⅎ𝑦𝐴 | |
2 | nfra1 2443 | . 2 ⊢ Ⅎ𝑦∀𝑦 ∈ 𝐵 𝜑 | |
3 | 1, 2 | nfralxy 2448 | 1 ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1421 ∀wral 2393 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 |
This theorem is referenced by: invdisj 3893 reusv3 4351 |
Copyright terms: Public domain | W3C validator |