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Mirrors > Home > MPE Home > Th. List > nfexOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nfex 2154 as of 16-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfexOLD.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfexOLD | ⊢ Ⅎ𝑥∃𝑦𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfexOLD.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | nf5ri 2065 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) |
3 | 2 | hbexOLD 2152 | . 2 ⊢ (∃𝑦𝜑 → ∀𝑥∃𝑦𝜑) |
4 | 3 | nf5i 2024 | 1 ⊢ Ⅎ𝑥∃𝑦𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1704 Ⅎwnf 1708 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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