Theorem simp33r 1318

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 1219	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1151	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by:  totprob  34734  cdleme19b  40940  cdleme19e  40943  cdleme20h  40952  cdleme20l2  40957  cdleme20m  40959  cdleme21d  40966  cdleme21e  40967  cdleme22eALTN  40981  cdleme22f2  40983  cdleme22g  40984  cdleme26e  40995  cdleme37m  41098  cdlemeg46gfre  41168  cdlemg28a  41329  cdlemg28b  41339  cdlemk5a  41471  cdlemk6  41473