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Metamath Proof Explorer
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012)
|
|
Ref |
Expression |
|
Assertion |
simp23r |
⊢ ( ( 𝜏 ∧ ( 𝜒 ∧ 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ) ∧ 𝜂 ) → 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
simp3r |
⊢ ( ( 𝜒 ∧ 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜓 ) |
| 2 |
1
|
3ad2ant2 |
⊢ ( ( 𝜏 ∧ ( 𝜒 ∧ 𝜃 ∧ ( 𝜑 ∧ 𝜓 ) ) ∧ 𝜂 ) → 𝜓 ) |