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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 1310 | . 2 ⊢ (⊥ → 𝜓) | |
2 | 1 | adantl 272 | 1 ⊢ ((𝜑 ∧ ⊥) → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ⊥wfal 1301 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-fal 1302 |
This theorem is referenced by: bj-axemptylem 12500 |
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