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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfdiOLD | Structured version Visualization version GIF version |
Description: Obsolete proof temporarily kept here in view of the change of nf5 2102 to df-nf 1701. (Contributed by NM, 8-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bj-nfdiOLD.nf | ⊢ (𝜑 → Ⅎ𝑥𝜑) |
Ref | Expression |
---|---|
bj-nfdiOLD | ⊢ Ⅎ𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8a 2039 | . . 3 ⊢ (𝜑 → ∃𝑥𝜑) | |
2 | bj-nfdiOLD.nf | . . . 4 ⊢ (𝜑 → Ⅎ𝑥𝜑) | |
3 | df-nf 1701 | . . . 4 ⊢ (Ⅎ𝑥𝜑 ↔ (∃𝑥𝜑 → ∀𝑥𝜑)) | |
4 | 2, 3 | sylib 207 | . . 3 ⊢ (𝜑 → (∃𝑥𝜑 → ∀𝑥𝜑)) |
5 | 1, 4 | mpd 15 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) |
6 | 5 | nf5i 2011 | 1 ⊢ Ⅎ𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 ∃wex 1695 Ⅎwnf 1699 |
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-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nf 1701 |
This theorem is referenced by: (None) |
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