Theorem simp33r 1299

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 1200	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant3 1133	1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓)

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  32294  cdleme19b  38245  cdleme19e  38248  cdleme20h  38257  cdleme20l2  38262  cdleme20m  38264  cdleme21d  38271  cdleme21e  38272  cdleme22eALTN  38286  cdleme22f2  38288  cdleme22g  38289  cdleme26e  38300  cdleme37m  38403  cdlemeg46gfre  38473  cdlemg28a  38634  cdlemg28b  38644  cdlemk5a  38776  cdlemk6  38778