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Mirrors > Home > MPE Home > Th. List > 19.3OLD | Structured version Visualization version GIF version |
Description: Obsolete proof of 19.3 2069 as of 6-Oct-2021. (Contributed by NM, 12-Mar-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
19.3OLD.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
19.3OLD | ⊢ (∀𝑥𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 2053 | . 2 ⊢ (∀𝑥𝜑 → 𝜑) | |
2 | 19.3OLD.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | nfriOLD 2189 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) |
4 | 1, 3 | impbii 199 | 1 ⊢ (∀𝑥𝜑 ↔ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 196 ∀wal 1481 ℲwnfOLD 1709 |
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-12 2047 |
This theorem depends on definitions: df-bi 197 df-ex 1705 df-nfOLD 1721 |
This theorem is referenced by: 19.27OLD 2234 19.28OLD 2235 |
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