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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-vtoclgf | GIF version |
Description: Weakening two hypotheses of vtoclgf 2668. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
bj-vtoclgf.nf1 | ⊢ Ⅎ𝑥𝐴 |
bj-vtoclgf.nf2 | ⊢ Ⅎ𝑥𝜓 |
bj-vtoclgf.min | ⊢ (𝑥 = 𝐴 → 𝜑) |
bj-vtoclgf.maj | ⊢ (𝑥 = 𝐴 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
bj-vtoclgf | ⊢ (𝐴 ∈ 𝑉 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-vtoclgf.nf1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
2 | bj-vtoclgf.nf2 | . . 3 ⊢ Ⅎ𝑥𝜓 | |
3 | bj-vtoclgf.min | . . 3 ⊢ (𝑥 = 𝐴 → 𝜑) | |
4 | 1, 2, 3 | bj-vtoclgft 11017 | . 2 ⊢ (∀𝑥(𝑥 = 𝐴 → (𝜑 → 𝜓)) → (𝐴 ∈ 𝑉 → 𝜓)) |
5 | bj-vtoclgf.maj | . 2 ⊢ (𝑥 = 𝐴 → (𝜑 → 𝜓)) | |
6 | 4, 5 | mpg 1381 | 1 ⊢ (𝐴 ∈ 𝑉 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1285 Ⅎwnf 1390 ∈ wcel 1434 Ⅎwnfc 2210 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-v 2614 |
This theorem is referenced by: elabgf2 11022 |
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