Theorem simp33r 1320

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 1221	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1153	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  totprob  34946  cdleme19b  41185  cdleme19e  41188  cdleme20h  41197  cdleme20l2  41202  cdleme20m  41204  cdleme21d  41211  cdleme21e  41212  cdleme22eALTN  41226  cdleme22f2  41228  cdleme22g  41229  cdleme26e  41240  cdleme37m  41343  cdlemeg46gfre  41413  cdlemg28a  41574  cdlemg28b  41584  cdlemk5a  41716  cdlemk6  41718