Theorem simp31r 1277

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 1178	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) → 𝜓)
2	1	3ad2ant3 1115	1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 387   ∧ w3a 1068

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 199  df-an 388  df-3an 1070

This theorem is referenced by:  ps-2c  36057  cdlema1N  36320  cdlemednpq  36828  cdleme19e  36836  cdleme20h  36845  cdleme20j  36847  cdleme20l2  36850  cdleme20m  36852  cdleme22a  36869  cdleme22cN  36871  cdleme22f2  36876  cdleme26f2ALTN  36893  cdleme37m  36991  cdlemg12f  37177  cdlemg12g  37178  cdlemg12  37179  cdlemg28a  37222  cdlemg29  37234  cdlemg33a  37235  cdlemg36  37243  cdlemk16a  37385  cdlemk21-2N  37420  cdlemk54  37487  dihord10  37752