Theorem simp13 1031

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

Assertion

Ref	Expression
simp13	⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)

Proof of Theorem simp13

Step	Hyp	Ref	Expression
1		simp3 1001	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
2	1	3ad2ant1 1020	1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒)

Syntax hints:   → wi 4   ∧ w3a 980

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 982

This theorem is referenced by:  simpl13  1076  simpr13  1085  simp113  1130  simp213  1139  simp313  1148  funtpg  5310  dvdsgcd  12204  coprimeprodsq  12451  pythagtriplem4  12462  pythagtriplem13  12470  pythagtriplem14  12471  pythagtriplem16  12473  pythagtrip  12477