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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 124 | 1 ⊢ (𝜑 ↔ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: biidd 170 3anbi1i 1129 3anbi2i 1130 3anbi3i 1131 trubitru 1346 falbifal 1349 eqid 2081 abid2 2199 abid2f 2243 ceqsexg 2723 nnwetri 6382 |
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