Theorem simp123 1306

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 1207	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜒)
2	1	3ad2ant1 1132	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  28961  axpasch  28971  exatleN  39387  ps-2b  39465  3atlem1  39466  3atlem2  39467  3atlem4  39469  3atlem5  39470  3atlem6  39471  2llnjaN  39549  2llnjN  39550  4atlem12b  39594  2lplnja  39602  2lplnj  39603  dalemrea  39611  dath2  39720  lneq2at  39761  osumcllem7N  39945  cdleme26ee  40343  cdlemg35  40696  cdlemg36  40697  cdlemj1  40804  cdlemk23-3  40885  cdlemk25-3  40887  cdlemk26b-3  40888  cdlemk27-3  40890  cdlemk28-3  40891  cdleml3N  40961  iscnrm3llem2  48747