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Mirrors > Home > MPE Home > Th. List > 19.9hOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of 19.9h 2120 as of 6-Oct-2021. (Contributed by FL, 24-Mar-2007.) (Proof shortened by Wolf Lammen, 5-Jan-2018.) (Proof shortened by Wolf Lammen, 14-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
19.9hOLD.1 | ⊢ (𝜑 → ∀𝑥𝜑) |
Ref | Expression |
---|---|
19.9hOLD | ⊢ (∃𝑥𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.9hOLD.1 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | 1 | nfiOLD 1734 | . 2 ⊢ Ⅎ𝑥𝜑 |
3 | 2 | 19.9OLD 2205 | 1 ⊢ (∃𝑥𝜑 ↔ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 ∀wal 1481 ∃wex 1704 |
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-12 2047 |
This theorem depends on definitions: df-bi 197 df-ex 1705 df-nfOLD 1721 |
This theorem is referenced by: (None) |
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