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  34461  cdleme19b  40423  cdleme19e  40426  cdleme20h  40435  cdleme20l2  40440  cdleme20m  40442  cdleme21d  40449  cdleme21e  40450  cdleme22eALTN  40464  cdleme22f2  40466  cdleme22g  40467  cdleme26e  40478  cdleme37m  40581  cdlemeg46gfre  40651  cdlemg28a  40812  cdlemg28b  40822  cdlemk5a  40954  cdlemk6  40956