Theorem simp33r 1302

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 1203	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 1088

This theorem is referenced by:  totprob  34584  cdleme19b  40560  cdleme19e  40563  cdleme20h  40572  cdleme20l2  40577  cdleme20m  40579  cdleme21d  40586  cdleme21e  40587  cdleme22eALTN  40601  cdleme22f2  40603  cdleme22g  40604  cdleme26e  40615  cdleme37m  40718  cdlemeg46gfre  40788  cdlemg28a  40949  cdlemg28b  40959  cdlemk5a  41091  cdlemk6  41093