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Mirrors > Home > ILE Home > Th. List > 2th | GIF version |
Description: Two truths are equivalent. (Contributed by NM, 18-Aug-1993.) |
Ref | Expression |
---|---|
2th.1 | ⊢ 𝜑 |
2th.2 | ⊢ 𝜓 |
Ref | Expression |
---|---|
2th | ⊢ (𝜑 ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2th.2 | . . 3 ⊢ 𝜓 | |
2 | 1 | a1i 9 | . 2 ⊢ (𝜑 → 𝜓) |
3 | 2th.1 | . . 3 ⊢ 𝜑 | |
4 | 3 | a1i 9 | . 2 ⊢ (𝜓 → 𝜑) |
5 | 2, 4 | impbii 125 | 1 ⊢ (𝜑 ↔ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: trujust 1334 dftru2 1340 bitru 1344 vjust 2690 pwv 3743 int0 3793 0iin 3879 snnex 4377 ruv 4473 fo1st 6063 fo2nd 6064 eqer 6469 ener 6681 rexfiuz 10793 bdth 13200 |
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