![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > simp3bi | GIF version |
Description: Deduce a conjunct from a triple conjunction. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
3simp1bi.1 | ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃)) |
Ref | Expression |
---|---|
simp3bi | ⊢ (𝜑 → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3simp1bi.1 | . . 3 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃)) | |
2 | 1 | biimpi 113 | . 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒 ∧ 𝜃)) |
3 | 2 | simp3d 918 | 1 ⊢ (𝜑 → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 98 ∧ w3a 885 |
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 df-3an 887 |
This theorem is referenced by: limuni 4133 smores2 5909 ersym 6118 ertr 6121 eluzle 8485 |
Copyright terms: Public domain | W3C validator |