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Mirrors > Home > MPE Home > Th. List > trud | Structured version Visualization version GIF version |
Description: Eliminate ⊤ as an antecedent. A proposition implied by ⊤ is true. (Contributed by Mario Carneiro, 13-Mar-2014.) |
Ref | Expression |
---|---|
trud.1 | ⊢ (⊤ → 𝜑) |
Ref | Expression |
---|---|
trud | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1479 | . 2 ⊢ ⊤ | |
2 | trud.1 | . 2 ⊢ (⊤ → 𝜑) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ 𝜑 |
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