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  39547  cdlema1N  39810  cdlemednpq  40318  cdleme19e  40326  cdleme20h  40335  cdleme20j  40337  cdleme20l2  40340  cdleme20m  40342  cdleme22a  40359  cdleme22cN  40361  cdleme22f2  40366  cdleme26f2ALTN  40383  cdleme37m  40481  cdlemg12f  40667  cdlemg12g  40668  cdlemg12  40669  cdlemg28a  40712  cdlemg29  40724  cdlemg33a  40725  cdlemg36  40733  cdlemk16a  40875  cdlemk21-2N  40910  cdlemk54  40977  dihord10  41242