Theorem simp11 1054

Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.)

Assertion

Ref	Expression
simp11	⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Proof of Theorem simp11

Step	Hyp	Ref	Expression
1		simp1 1024	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜑)
2	1	3ad2ant1 1045	1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑)

Syntax hints:   → wi 4   ∧ w3a 1005

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1007

This theorem is referenced by:  simpl11  1099  simpr11  1108  simp111  1153  simp211  1162  simp311  1171  frecsuclem  6615  coprimeprodsq  12891  pythagtriplem14  12911  pythagtrip  12917  clwwlknonex2  16360