Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > simp222 | GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp222 | ⊢ ((𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp22 1021 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓) | |
2 | 1 | 3ad2ant2 1009 | 1 ⊢ ((𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 968 |
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 df-3an 970 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |