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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfnfc | Structured version Visualization version GIF version |
Description: Remove dependency on ax-ext 2602 (and df-cleq 2615) from nfnfc 2774. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nfnfc.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
bj-nfnfc | ⊢ Ⅎ𝑥Ⅎ𝑦𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nfc 2753 | . 2 ⊢ (Ⅎ𝑦𝐴 ↔ ∀𝑧Ⅎ𝑦 𝑧 ∈ 𝐴) | |
2 | bj-nfnfc.1 | . . . . 5 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | bj-nfcri 32852 | . . . 4 ⊢ Ⅎ𝑥 𝑧 ∈ 𝐴 |
4 | 3 | nfnf 2158 | . . 3 ⊢ Ⅎ𝑥Ⅎ𝑦 𝑧 ∈ 𝐴 |
5 | 4 | nfal 2153 | . 2 ⊢ Ⅎ𝑥∀𝑧Ⅎ𝑦 𝑧 ∈ 𝐴 |
6 | 1, 5 | nfxfr 1779 | 1 ⊢ Ⅎ𝑥Ⅎ𝑦𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1481 Ⅎwnf 1708 ∈ wcel 1990 Ⅎwnfc 2751 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clel 2618 df-nfc 2753 |
This theorem is referenced by: (None) |
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