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Mirrors > Home > MPE Home > Th. List > 19.9OLD | Structured version Visualization version GIF version |
Description: Obsolete proof of 19.9 2060 as of 6-Oct-2021. (Contributed by FL, 24-Mar-2007.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) Revised to shorten other proofs. (Revised by Wolf Lammen, 14-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
19.9OLD.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
19.9OLD | ⊢ (∃𝑥𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.9OLD.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | 19.9tOLD 2192 | . 2 ⊢ (Ⅎ𝑥𝜑 → (∃𝑥𝜑 ↔ 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (∃𝑥𝜑 ↔ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ∃wex 1695 ℲwnfOLD 1700 |
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-nfOLD 1712 |
This theorem is referenced by: 19.9hOLD 2194 exlimdOLD 2211 |
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