Theorem simp123 1309

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 1210	. 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 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  29014  axpasch  29024  exatleN  39864  ps-2b  39942  3atlem1  39943  3atlem2  39944  3atlem4  39946  3atlem5  39947  3atlem6  39948  2llnjaN  40026  2llnjN  40027  4atlem12b  40071  2lplnja  40079  2lplnj  40080  dalemrea  40088  dath2  40197  lneq2at  40238  osumcllem7N  40422  cdleme26ee  40820  cdlemg35  41173  cdlemg36  41174  cdlemj1  41281  cdlemk23-3  41362  cdlemk25-3  41364  cdlemk26b-3  41365  cdlemk27-3  41367  cdlemk28-3  41368  cdleml3N  41438  iscnrm3llem2  49437