Theorem simp322 1326

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

Assertion

Ref	Expression
simp322	⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓)

Proof of Theorem simp322

Step	Hyp	Ref	Expression
1		simp22 1209	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓)
2	1	3ad2ant3 1136	1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 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:  dalemqnet  39949  dalemrot  39954  dath2  40034  cdleme18d  40592  cdleme20i  40614  cdleme20j  40615  cdleme20l2  40618  cdleme20l  40619  cdleme20m  40620  cdleme20  40621  cdleme21j  40633  cdleme22eALTN  40642  cdleme26eALTN  40658  cdlemk16a  41153  cdlemk12u-2N  41187  cdlemk21-2N  41188  cdlemk22  41190  cdlemk31  41193  cdlemk32  41194  cdlemk11ta  41226  cdlemk11tc  41242