Theorem simp333 1326

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

Assertion

Ref	Expression
simp333	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simp333

Step	Hyp	Ref	Expression
1		simp33 1209	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant3 1133	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

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:  ivthALT  34503  dalemclrju  37629  dath2  37730  cdlema1N  37784  cdleme26eALTN  38354  cdlemk7u  38863  cdlemk11u  38864  cdlemk12u  38865  cdlemk22  38886  cdlemk23-3  38895  cdlemk33N  38902  cdlemk11ta  38922  cdlemk11tc  38938  cdlemk54  38951