Mathbox for Jarvin Udandy |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > aibnbaif | Structured version Visualization version GIF version |
Description: Given a implies b, not b, there exists a proof for a is F. (Contributed by Jarvin Udandy, 1-Sep-2016.) |
Ref | Expression |
---|---|
aibnbaif.1 | ⊢ (𝜑 → 𝜓) |
aibnbaif.2 | ⊢ ¬ 𝜓 |
Ref | Expression |
---|---|
aibnbaif | ⊢ (𝜑 ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aibnbaif.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | aibnbaif.2 | . . 3 ⊢ ¬ 𝜓 | |
3 | 1, 2 | aibnbna 43940 | . 2 ⊢ ¬ 𝜑 |
4 | 3 | bifal 1558 | 1 ⊢ (𝜑 ↔ ⊥) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 209 ⊥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 210 df-tru 1545 df-fal 1555 |
This theorem is referenced by: conimpf 43951 conimpfalt 43952 dandysum2p2e4 44032 |
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