Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > anabsan2 | GIF version |
Description: Absorption of antecedent with conjunction. (Contributed by NM, 10-May-2004.) (Revised by NM, 1-Jan-2013.) |
Ref | Expression |
---|---|
anabsan2.1 | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜓)) → 𝜒) |
Ref | Expression |
---|---|
anabsan2 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anabsan2.1 | . . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜓)) → 𝜒) | |
2 | 1 | an12s 499 | . 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜓)) → 𝜒) |
3 | 2 | anabss7 517 | 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: anabss3 519 anandirs 527 |
Copyright terms: Public domain | W3C validator |