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Mirrors > Home > MPE Home > Th. List > nfbiOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nfbi 1833 as of 6-Oct-2021. (Contributed by NM, 26-May-1993.) (Revised by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 2-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
nfOLD.1 | ⊢ Ⅎ𝑥𝜑 |
nfOLD.2 | ⊢ Ⅎ𝑥𝜓 |
Ref | Expression |
---|---|
nfbiOLD | ⊢ Ⅎ𝑥(𝜑 ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfOLD.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
3 | nfOLD.2 | . . . 4 ⊢ Ⅎ𝑥𝜓 | |
4 | 3 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜓) |
5 | 2, 4 | nfbidOLD 2242 | . 2 ⊢ (⊤ → Ⅎ𝑥(𝜑 ↔ 𝜓)) |
6 | 5 | trud 1493 | 1 ⊢ Ⅎ𝑥(𝜑 ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 196 ⊤wtru 1484 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-10 2019 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-nfOLD 1721 |
This theorem is referenced by: (None) |
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