Theorem simp313 1323

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

Assertion

Ref	Expression
simp313	⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜒)

Proof of Theorem simp313

Step	Hyp	Ref	Expression
1		simp13 1206	. 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)
2	1	3ad2ant3 1136	1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜒)

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  39659  dalem5  39669  dalem-cly  39673  dath2  39739  cdleme26e  40361  cdleme38m  40465  cdleme38n  40466  cdlemg28b  40705  cdlemg28  40706  cdlemk7  40850  cdlemk11  40851  cdlemk12  40852  cdlemk7u  40872  cdlemk11u  40873  cdlemk12u  40874  cdlemk22  40895  cdlemk23-3  40904  cdlemk25-3  40906