Theorem simp121 1306

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp121	⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜑)

Proof of Theorem simp121

Step	Hyp	Ref	Expression
1		simp21 1207	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑)
2	1	3ad2ant1 1133	1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜂 ∧ 𝜁) → 𝜑)

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  28915  axpasch  28925  exatleN  39428  ps-2b  39506  3atlem1  39507  3atlem2  39508  3atlem4  39510  3atlem5  39511  3atlem6  39512  2llnjaN  39590  4atlem12b  39635  2lplnja  39643  dalempea  39650  dath2  39761  lneq2at  39802  llnexchb2  39893  dalawlem1  39895  osumcllem7N  39986  lhpexle3lem  40035  cdleme26ee  40384  cdlemg34  40736  cdlemg36  40738  cdlemj1  40845  cdlemj2  40846  cdlemk23-3  40926  cdlemk25-3  40928  cdlemk26b-3  40929  cdlemk26-3  40930  cdlemk27-3  40931  cdleml3N  41002  iscnrm3llem2  48891