Theorem simp123 1307

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 1208	. 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 1087

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 1089

This theorem is referenced by:  ax5seglem3  28964  axpasch  28974  exatleN  39361  ps-2b  39439  3atlem1  39440  3atlem2  39441  3atlem4  39443  3atlem5  39444  3atlem6  39445  2llnjaN  39523  2llnjN  39524  4atlem12b  39568  2lplnja  39576  2lplnj  39577  dalemrea  39585  dath2  39694  lneq2at  39735  osumcllem7N  39919  cdleme26ee  40317  cdlemg35  40670  cdlemg36  40671  cdlemj1  40778  cdlemk23-3  40859  cdlemk25-3  40861  cdlemk26b-3  40862  cdlemk27-3  40864  cdlemk28-3  40865  cdleml3N  40935  iscnrm3llem2  48630