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 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  34429  cdleme19b  40306  cdleme19e  40309  cdleme20h  40318  cdleme20l2  40323  cdleme20m  40325  cdleme21d  40332  cdleme21e  40333  cdleme22eALTN  40347  cdleme22f2  40349  cdleme22g  40350  cdleme26e  40361  cdleme37m  40464  cdlemeg46gfre  40534  cdlemg28a  40695  cdlemg28b  40705  cdlemk5a  40837  cdlemk6  40839