Theorem simp31r 1298

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp31r	⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Proof of Theorem simp31r

Step	Hyp	Ref	Expression
1		simp1r 1199	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) → 𝜓)
2	1	3ad2ant3 1135	1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 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:  ps-2c  39529  cdlema1N  39792  cdlemednpq  40300  cdleme19e  40308  cdleme20h  40317  cdleme20j  40319  cdleme20l2  40322  cdleme20m  40324  cdleme22a  40341  cdleme22cN  40343  cdleme22f2  40348  cdleme26f2ALTN  40365  cdleme37m  40463  cdlemg12f  40649  cdlemg12g  40650  cdlemg12  40651  cdlemg28a  40694  cdlemg29  40706  cdlemg33a  40707  cdlemg36  40715  cdlemk16a  40857  cdlemk21-2N  40892  cdlemk54  40959  dihord10  41224