Theorem simp133 1308

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

Assertion

Ref	Expression
simp133	⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Proof of Theorem simp133

Step	Hyp	Ref	Expression
1		simp33 1209	. 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	3ad2ant1 1131	1 ⊢ (((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ 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:  tsmsxp  23214  ax5seglem3  27202  exatleN  37345  3atlem1  37424  3atlem2  37425  3atlem6  37429  4atlem11b  37549  4atlem12b  37552  lplncvrlvol2  37556  dalemuea  37572  dath2  37678  4atexlemex6  38015  cdleme22f2  38288  cdleme22g  38289  cdlemg7aN  38566  cdlemg31c  38640  cdlemg36  38655  cdlemj1  38762  cdlemj2  38763  cdlemk23-3  38843  cdlemk26b-3  38846