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  34587  cdleme19b  40764  cdleme19e  40767  cdleme20h  40776  cdleme20l2  40781  cdleme20m  40783  cdleme21d  40790  cdleme21e  40791  cdleme22eALTN  40805  cdleme22f2  40807  cdleme22g  40808  cdleme26e  40819  cdleme37m  40922  cdlemeg46gfre  40992  cdlemg28a  41153  cdlemg28b  41163  cdlemk5a  41295  cdlemk6  41297