Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > simp23 | Structured version Visualization version GIF version |
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.) |
Ref | Expression |
---|---|
simp23 | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3 1139 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜃) | |
2 | 1 | 3ad2ant2 1135 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃) ∧ 𝜏) → 𝜃) |
Copyright terms: Public domain | W3C validator |