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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 117 | 1 ⊢ (𝜑 ↔ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: biidd 161 3anbi1i 1095 3anbi2i 1096 3anbi3i 1097 trubitru 1306 falbifal 1309 eqid 2040 abid2 2158 abid2f 2202 ceqsexg 2672 nnwetri 6354 |
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