Theorem simp33r 1298

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 1199	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1132	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 394   ∧ w3a 1084

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 395  df-3an 1086

This theorem is referenced by:  totprob  34080  cdleme19b  39809  cdleme19e  39812  cdleme20h  39821  cdleme20l2  39826  cdleme20m  39828  cdleme21d  39835  cdleme21e  39836  cdleme22eALTN  39850  cdleme22f2  39852  cdleme22g  39853  cdleme26e  39864  cdleme37m  39967  cdlemeg46gfre  40037  cdlemg28a  40198  cdlemg28b  40208  cdlemk5a  40340  cdlemk6  40342