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Mirrors > Home > MPE Home > Th. List > Mathboxes > efald2 | Structured version Visualization version GIF version |
Description: A proof by contradiction. (Contributed by Giovanni Mascellani, 15-Sep-2017.) |
Ref | Expression |
---|---|
efald2.1 | ⊢ (¬ 𝜑 → ⊥) |
Ref | Expression |
---|---|
efald2 | ⊢ 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | efald2.1 | . . . 4 ⊢ (¬ 𝜑 → ⊥) | |
2 | 1 | adantl 482 | . . 3 ⊢ ((⊤ ∧ ¬ 𝜑) → ⊥) |
3 | 2 | efald 1563 | . 2 ⊢ (⊤ → 𝜑) |
4 | 3 | mptru 1549 | 1 ⊢ 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ⊤wtru 1543 ⊥wfal 1554 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1545 df-fal 1555 |
This theorem is referenced by: mpobi123f 36316 mptbi12f 36320 ac6s6 36326 |
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