Theorem simp33r 1301

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 1202	. 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 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  34392  cdleme19b  40261  cdleme19e  40264  cdleme20h  40273  cdleme20l2  40278  cdleme20m  40280  cdleme21d  40287  cdleme21e  40288  cdleme22eALTN  40302  cdleme22f2  40304  cdleme22g  40305  cdleme26e  40316  cdleme37m  40419  cdlemeg46gfre  40489  cdlemg28a  40650  cdlemg28b  40660  cdlemk5a  40792  cdlemk6  40794