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  39573  cdlema1N  39836  cdlemednpq  40344  cdleme19e  40352  cdleme20h  40361  cdleme20j  40363  cdleme20l2  40366  cdleme20m  40368  cdleme22a  40385  cdleme22cN  40387  cdleme22f2  40392  cdleme26f2ALTN  40409  cdleme37m  40507  cdlemg12f  40693  cdlemg12g  40694  cdlemg12  40695  cdlemg28a  40738  cdlemg29  40750  cdlemg33a  40751  cdlemg36  40759  cdlemk16a  40901  cdlemk21-2N  40936  cdlemk54  41003  dihord10  41268