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  28865  axpasch  28875  exatleN  39405  ps-2b  39483  3atlem1  39484  3atlem2  39485  3atlem4  39487  3atlem5  39488  3atlem6  39489  2llnjaN  39567  4atlem12b  39612  2lplnja  39620  dalempea  39627  dath2  39738  lneq2at  39779  llnexchb2  39870  dalawlem1  39872  osumcllem7N  39963  lhpexle3lem  40012  cdleme26ee  40361  cdlemg34  40713  cdlemg36  40715  cdlemj1  40822  cdlemj2  40823  cdlemk23-3  40903  cdlemk25-3  40905  cdlemk26b-3  40906  cdlemk26-3  40907  cdlemk27-3  40908  cdleml3N  40979  iscnrm3llem2  48942