Theorem simp332 1324

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

Assertion

Ref	Expression
simp332	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Proof of Theorem simp332

Step	Hyp	Ref	Expression
1		simp32 1207	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓)
2	1	3ad2ant3 1132	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓)

Syntax hints:   → wi 4   ∧ w3a 1084

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 1086

This theorem is referenced by:  ivthALT  35728  dalemclqjt  39017  dath2  39119  cdlema1N  39173  cdleme26eALTN  39743  cdlemk7u  40252  cdlemk11u  40253  cdlemk12u  40254  cdlemk23-3  40284  cdlemk33N  40291  cdlemk11ta  40311  cdlemk11tc  40327  cdlemk54  40340