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Mirrors > Home > ILE Home > Th. List > falimd | GIF version |
Description: The truth value ⊥ implies anything. (Contributed by Mario Carneiro, 9-Feb-2017.) |
Ref | Expression |
---|---|
falimd | ⊢ ((𝜑 ∧ ⊥) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | falim 1362 | . 2 ⊢ (⊥ → 𝜓) | |
2 | 1 | adantl 275 | 1 ⊢ ((𝜑 ∧ ⊥) → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ⊥wfal 1353 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-fal 1354 |
This theorem is referenced by: bj-axemptylem 13892 |
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