Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfcrii | Structured version Visualization version GIF version |
Description: Remove dependency on ax-ext 2590 (and df-cleq 2603) from nfcrii 2744. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nfcri.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
bj-nfcrii | ⊢ (𝑦 ∈ 𝐴 → ∀𝑥 𝑦 ∈ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nfcri.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
2 | nfcr 2743 | . . . 4 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥 𝑧 ∈ 𝐴) | |
3 | 1, 2 | ax-mp 5 | . . 3 ⊢ Ⅎ𝑥 𝑧 ∈ 𝐴 |
4 | 3 | nf5ri 2053 | . 2 ⊢ (𝑧 ∈ 𝐴 → ∀𝑥 𝑧 ∈ 𝐴) |
5 | 4 | bj-hblem 32043 | 1 ⊢ (𝑦 ∈ 𝐴 → ∀𝑥 𝑦 ∈ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 Ⅎwnf 1699 ∈ wcel 1977 Ⅎwnfc 2738 |
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-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clel 2606 df-nfc 2740 |
This theorem is referenced by: bj-nfcri 32046 |
Copyright terms: Public domain | W3C validator |