Theorem simp312 1319

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 1202	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1133	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1085

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 206  df-an 396  df-3an 1087

This theorem is referenced by:  dalemrot  39054  dalem-cly  39068  dath2  39134  cdleme26e  39756  cdleme38m  39860  cdleme38n  39861  cdleme39n  39863  cdlemg28b  40100  cdlemk7  40245  cdlemk11  40246  cdlemk12  40247  cdlemk7u  40267  cdlemk11u  40268  cdlemk12u  40269  cdlemk22  40290  cdlemk23-3  40299  cdlemk25-3  40301