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 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  34409  cdleme19b  40287  cdleme19e  40290  cdleme20h  40299  cdleme20l2  40304  cdleme20m  40306  cdleme21d  40313  cdleme21e  40314  cdleme22eALTN  40328  cdleme22f2  40330  cdleme22g  40331  cdleme26e  40342  cdleme37m  40445  cdlemeg46gfre  40515  cdlemg28a  40676  cdlemg28b  40686  cdlemk5a  40818  cdlemk6  40820