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  39650  cdlema1N  39913  cdlemednpq  40421  cdleme19e  40429  cdleme20h  40438  cdleme20j  40440  cdleme20l2  40443  cdleme20m  40445  cdleme22a  40462  cdleme22cN  40464  cdleme22f2  40469  cdleme26f2ALTN  40486  cdleme37m  40584  cdlemg12f  40770  cdlemg12g  40771  cdlemg12  40772  cdlemg28a  40815  cdlemg29  40827  cdlemg33a  40828  cdlemg36  40836  cdlemk16a  40978  cdlemk21-2N  41013  cdlemk54  41080  dihord10  41345