Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > anabsan | GIF version |
Description: Absorption of antecedent with conjunction. (Contributed by NM, 24-Mar-1996.) (Revised by NM, 18-Nov-2013.) |
Ref | Expression |
---|---|
anabsan.1 | ⊢ (((𝜑 ∧ 𝜑) ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
anabsan | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.24 375 | . 2 ⊢ (𝜑 ↔ (𝜑 ∧ 𝜑)) | |
2 | anabsan.1 | . 2 ⊢ (((𝜑 ∧ 𝜑) ∧ 𝜓) → 𝜒) | |
3 | 1, 2 | sylanb 268 | 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: anabss1 510 anabss5 512 anandis 526 |
Copyright terms: Public domain | W3C validator |