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Mirrors > Home > MPE Home > Th. List > 19.23hOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of 19.23h 2122 as of 6-Oct-2021. (Contributed by NM, 24-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 1-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
19.23hOLD.1 | ⊢ (𝜓 → ∀𝑥𝜓) |
Ref | Expression |
---|---|
19.23hOLD | ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.23hOLD.1 | . . 3 ⊢ (𝜓 → ∀𝑥𝜓) | |
2 | 1 | nfiOLD 1734 | . 2 ⊢ Ⅎ𝑥𝜓 |
3 | 2 | 19.23OLD 2219 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓)) |
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-or 385 df-ex 1705 df-nf 1710 df-nfOLD 1721 |
This theorem is referenced by: (None) |
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