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  34459  cdleme19b  40323  cdleme19e  40326  cdleme20h  40335  cdleme20l2  40340  cdleme20m  40342  cdleme21d  40349  cdleme21e  40350  cdleme22eALTN  40364  cdleme22f2  40366  cdleme22g  40367  cdleme26e  40378  cdleme37m  40481  cdlemeg46gfre  40551  cdlemg28a  40712  cdlemg28b  40722  cdlemk5a  40854  cdlemk6  40856