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Mirrors > Home > ILE Home > Th. List > anabss3 | GIF version |
Description: Absorption of antecedent into conjunction. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 1-Jan-2013.) |
Ref | Expression |
---|---|
anabss3.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
anabss3 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anabss3.1 | . . 3 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜓) → 𝜒) | |
2 | 1 | anasss 379 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜓)) → 𝜒) |
3 | 2 | anabsan2 518 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: 3anidm23 1194 expclzaplem 9279 |
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