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 1134	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 1088

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 398  df-3an 1090

This theorem is referenced by:  ax5seglem3  28189  axpasch  28199  exatleN  38275  ps-2b  38353  3atlem1  38354  3atlem2  38355  3atlem4  38357  3atlem5  38358  3atlem6  38359  2llnjaN  38437  2llnjN  38438  4atlem12b  38482  2lplnja  38490  2lplnj  38491  dalemrea  38499  dath2  38608  lneq2at  38649  osumcllem7N  38833  cdleme26ee  39231  cdlemg35  39584  cdlemg36  39585  cdlemj1  39692  cdlemk23-3  39773  cdlemk25-3  39775  cdlemk26b-3  39776  cdlemk27-3  39778  cdlemk28-3  39779  cdleml3N  39849  iscnrm3llem2  47583