Theorem simp33r 1303

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 1204	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1136	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ 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:  totprob  34604  cdleme19b  40674  cdleme19e  40677  cdleme20h  40686  cdleme20l2  40691  cdleme20m  40693  cdleme21d  40700  cdleme21e  40701  cdleme22eALTN  40715  cdleme22f2  40717  cdleme22g  40718  cdleme26e  40729  cdleme37m  40832  cdlemeg46gfre  40902  cdlemg28a  41063  cdlemg28b  41073  cdlemk5a  41205  cdlemk6  41207