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  34418  cdleme19b  40298  cdleme19e  40301  cdleme20h  40310  cdleme20l2  40315  cdleme20m  40317  cdleme21d  40324  cdleme21e  40325  cdleme22eALTN  40339  cdleme22f2  40341  cdleme22g  40342  cdleme26e  40353  cdleme37m  40456  cdlemeg46gfre  40526  cdlemg28a  40687  cdlemg28b  40697  cdlemk5a  40829  cdlemk6  40831