Theorem simp31r 1389

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 1248	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) → 𝜓)
2	1	3ad2ant3 1158	1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 384   ∧ w3a 1100

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 198  df-an 385  df-3an 1102

This theorem is referenced by:  ps-2c  35302  cdlema1N  35565  cdlemednpq  36074  cdleme19e  36082  cdleme20h  36091  cdleme20j  36093  cdleme20l2  36096  cdleme20m  36098  cdleme22a  36115  cdleme22cN  36117  cdleme22f2  36122  cdleme26f2ALTN  36139  cdleme37m  36237  cdlemg12f  36423  cdlemg12g  36424  cdlemg12  36425  cdlemg28a  36468  cdlemg29  36480  cdlemg33a  36481  cdlemg36  36489  cdlemk16a  36631  cdlemk21-2N  36666  cdlemk54  36733  dihord10  36998