Theorem simp312 1321

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp312	⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓)

Proof of Theorem simp312

Step	Hyp	Ref	Expression
1		simp12 1204	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1135	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1087

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089

This theorem is referenced by:  dalemrot  39614  dalem-cly  39628  dath2  39694  cdleme26e  40316  cdleme38m  40420  cdleme38n  40421  cdleme39n  40423  cdlemg28b  40660  cdlemk7  40805  cdlemk11  40806  cdlemk12  40807  cdlemk7u  40827  cdlemk11u  40828  cdlemk12u  40829  cdlemk22  40850  cdlemk23-3  40859  cdlemk25-3  40861