Theorem simp33r 1300

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 1201	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1134	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 396   ∧ 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 206  df-an 397  df-3an 1088

This theorem is referenced by:  totprob  32394  cdleme19b  38318  cdleme19e  38321  cdleme20h  38330  cdleme20l2  38335  cdleme20m  38337  cdleme21d  38344  cdleme21e  38345  cdleme22eALTN  38359  cdleme22f2  38361  cdleme22g  38362  cdleme26e  38373  cdleme37m  38476  cdlemeg46gfre  38546  cdlemg28a  38707  cdlemg28b  38717  cdlemk5a  38849  cdlemk6  38851