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Mirrors > Home > ILE Home > Th. List > biid | GIF version |
Description: Principle of identity for logical equivalence. Theorem *4.2 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
biid | ⊢ (𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (𝜑 → 𝜑) | |
2 | 1, 1 | impbii 125 | 1 ⊢ (𝜑 ↔ 𝜑) |
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: biidd 171 3anbi1i 1173 3anbi2i 1174 3anbi3i 1175 trubitru 1397 falbifal 1400 eqid 2157 abid2 2278 abid2f 2325 ceqsexg 2840 nnwetri 6860 exmidontriimlem3 7158 fsum2d 11332 fprod2d 11520 isstructim 12215 |
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