Theorem simp123 1308

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

Assertion

Ref	Expression
simp123	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Proof of Theorem simp123

Step	Hyp	Ref	Expression
1		simp23 1209	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant1 1133	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1086

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 207  df-an 396  df-3an 1088

This theorem is referenced by:  ax5seglem3  28858  axpasch  28868  exatleN  39398  ps-2b  39476  3atlem1  39477  3atlem2  39478  3atlem4  39480  3atlem5  39481  3atlem6  39482  2llnjaN  39560  2llnjN  39561  4atlem12b  39605  2lplnja  39613  2lplnj  39614  dalemrea  39622  dath2  39731  lneq2at  39772  osumcllem7N  39956  cdleme26ee  40354  cdlemg35  40707  cdlemg36  40708  cdlemj1  40815  cdlemk23-3  40896  cdlemk25-3  40898  cdlemk26b-3  40899  cdlemk27-3  40901  cdlemk28-3  40902  cdleml3N  40972  iscnrm3llem2  48938