Theorem simp33r 1298

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp33r	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Proof of Theorem simp33r

Step	Hyp	Ref	Expression
1		simp3r 1199	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1132	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1084

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 396  df-3an 1086

This theorem is referenced by:  totprob  33955  cdleme19b  39687  cdleme19e  39690  cdleme20h  39699  cdleme20l2  39704  cdleme20m  39706  cdleme21d  39713  cdleme21e  39714  cdleme22eALTN  39728  cdleme22f2  39730  cdleme22g  39731  cdleme26e  39742  cdleme37m  39845  cdlemeg46gfre  39915  cdlemg28a  40076  cdlemg28b  40086  cdlemk5a  40218  cdlemk6  40220