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  28865  axpasch  28875  exatleN  39405  ps-2b  39483  3atlem1  39484  3atlem2  39485  3atlem4  39487  3atlem5  39488  3atlem6  39489  2llnjaN  39567  2llnjN  39568  4atlem12b  39612  2lplnja  39620  2lplnj  39621  dalemrea  39629  dath2  39738  lneq2at  39779  osumcllem7N  39963  cdleme26ee  40361  cdlemg35  40714  cdlemg36  40715  cdlemj1  40822  cdlemk23-3  40903  cdlemk25-3  40905  cdlemk26b-3  40906  cdlemk27-3  40908  cdlemk28-3  40909  cdleml3N  40979  iscnrm3llem2  48942