Theorem simp31r 1295

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 1196	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) → 𝜓)
2	1	3ad2ant3 1133	1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃)) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 394   ∧ w3a 1085

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 206  df-an 395  df-3an 1087

This theorem is referenced by:  ps-2c  38702  cdlema1N  38965  cdlemednpq  39473  cdleme19e  39481  cdleme20h  39490  cdleme20j  39492  cdleme20l2  39495  cdleme20m  39497  cdleme22a  39514  cdleme22cN  39516  cdleme22f2  39521  cdleme26f2ALTN  39538  cdleme37m  39636  cdlemg12f  39822  cdlemg12g  39823  cdlemg12  39824  cdlemg28a  39867  cdlemg29  39879  cdlemg33a  39880  cdlemg36  39888  cdlemk16a  40030  cdlemk21-2N  40065  cdlemk54  40132  dihord10  40397