Theorem simp33l 1298

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

Assertion

Ref	Expression
simp33l	⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Proof of Theorem simp33l

Step	Hyp	Ref	Expression
1		simp3l 1199	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	3ad2ant3 1133	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 395   ∧ 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 396  df-3an 1087

This theorem is referenced by:  totprob  32373  cdleme19b  38297  cdleme19d  38299  cdleme19e  38300  cdleme20h  38309  cdleme20l2  38314  cdleme20m  38316  cdleme21d  38323  cdleme21e  38324  cdleme22e  38337  cdleme22f2  38340  cdleme22g  38341  cdleme26e  38352  cdleme28a  38363  cdleme28b  38364  cdleme37m  38455  cdleme39n  38459  cdlemeg46gfre  38525  cdlemg28a  38686  cdlemg28b  38696  cdlemk3  38826  cdlemk5a  38828  cdlemk6  38830  cdlemkuat  38859  cdlemkid2  38917