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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 2332 | . 2 ⊢ Ⅎ𝑦𝐴 | |
2 | nfra1 2521 | . 2 ⊢ Ⅎ𝑦∀𝑦 ∈ 𝐵 𝜑 | |
3 | 1, 2 | nfralxy 2528 | 1 ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1471 ∀wral 2468 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 |
This theorem is referenced by: invdisj 4012 reusv3 4475 |
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