Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > anabss5 | GIF version |
Description: Absorption of antecedent into conjunction. (Contributed by NM, 10-May-1994.) (Proof shortened by Wolf Lammen, 1-Jan-2013.) |
Ref | Expression |
---|---|
anabss5.1 | ⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) → 𝜒) |
Ref | Expression |
---|---|
anabss5 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anabss5.1 | . . 3 ⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) → 𝜒) | |
2 | 1 | anassrs 398 | . 2 ⊢ (((𝜑 ∧ 𝜑) ∧ 𝜓) → 𝜒) |
3 | 2 | anabsan 565 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: anabsi5 569 syl2an2r 585 mp3an2ani 1333 |
Copyright terms: Public domain | W3C validator |