Theorem simp33r 1314

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

Assertion

Ref	Expression
simp33r	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Proof of Theorem simp33r

Step	Hyp	Ref	Expression
1		simp3r 1215	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1147	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  totprob  34685  cdleme19b  40892  cdleme19e  40895  cdleme20h  40904  cdleme20l2  40909  cdleme20m  40911  cdleme21d  40918  cdleme21e  40919  cdleme22eALTN  40933  cdleme22f2  40935  cdleme22g  40936  cdleme26e  40947  cdleme37m  41050  cdlemeg46gfre  41120  cdlemg28a  41281  cdlemg28b  41291  cdlemk5a  41423  cdlemk6  41425