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Mirrors > Home > MPE Home > Th. List > iftrued | Structured version Visualization version GIF version |
Description: Value of the conditional operator when its first argument is true. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
iftrued.1 | ⊢ (𝜑 → 𝜒) |
Ref | Expression |
---|---|
iftrued | ⊢ (𝜑 → if(𝜒, 𝐴, 𝐵) = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iftrued.1 | . 2 ⊢ (𝜑 → 𝜒) | |
2 | iftrue 4042 | . 2 ⊢ (𝜒 → if(𝜒, 𝐴, 𝐵) = 𝐴) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → if(𝜒, 𝐴, 𝐵) = 𝐴) |
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