Theorem simp33r 1303

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 1204	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1136	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1087

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 1089

This theorem is referenced by:  totprob  34571  cdleme19b  40750  cdleme19e  40753  cdleme20h  40762  cdleme20l2  40767  cdleme20m  40769  cdleme21d  40776  cdleme21e  40777  cdleme22eALTN  40791  cdleme22f2  40793  cdleme22g  40794  cdleme26e  40805  cdleme37m  40908  cdlemeg46gfre  40978  cdlemg28a  41139  cdlemg28b  41149  cdlemk5a  41281  cdlemk6  41283