Theorem simp33r 1294

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 1195	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1128	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1080

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 208  df-an 397  df-3an 1082

This theorem is referenced by:  totprob  31298  cdleme19b  36992  cdleme19e  36995  cdleme20h  37004  cdleme20l2  37009  cdleme20m  37011  cdleme21d  37018  cdleme21e  37019  cdleme22eALTN  37033  cdleme22f2  37035  cdleme22g  37036  cdleme26e  37047  cdleme37m  37150  cdlemeg46gfre  37220  cdlemg28a  37381  cdlemg28b  37391  cdlemk5a  37523  cdlemk6  37525