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  28894  axpasch  28904  exatleN  39383  ps-2b  39461  3atlem1  39462  3atlem2  39463  3atlem4  39465  3atlem5  39466  3atlem6  39467  2llnjaN  39545  4atlem12b  39590  2lplnja  39598  dalempea  39605  dath2  39716  lneq2at  39757  llnexchb2  39848  dalawlem1  39850  osumcllem7N  39941  lhpexle3lem  39990  cdleme26ee  40339  cdlemg34  40691  cdlemg36  40693  cdlemj1  40800  cdlemj2  40801  cdlemk23-3  40881  cdlemk25-3  40883  cdlemk26b-3  40884  cdlemk26-3  40885  cdlemk27-3  40886  cdleml3N  40957  iscnrm3llem2  48935