Theorem simp1l 963

Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)

Assertion

Ref	Expression
simp1l	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) → 𝜑)

Proof of Theorem simp1l

Step	Hyp	Ref	Expression
1		simpl 107	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	3ad2ant1 960	1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒 ∧ 𝜃) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 102   ∧ w3a 920

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 922

This theorem is referenced by:  simpl1l  990  simpr1l  996  simp11l  1050  simp21l  1056  simp31l  1062  en2lp  4325  tfisi  4356  funprg  5000  nnsucsssuc  6156  ecopovtrn  6290  ecopovtrng  6293  addassnqg  6686  distrnqg  6691  ltsonq  6702  ltanqg  6704  ltmnqg  6705  distrnq0  6763  addassnq0  6766  mulasssrg  7049  distrsrg  7050  lttrsr  7053  ltsosr  7055  ltasrg  7061  mulextsr1lem  7070  mulextsr1  7071  axmulass  7153  axdistr  7154  dmdcanap  7929  lt2msq1  8082  ltdiv2  8084  lediv2  8088  modqdi  9526  expaddzaplem  9668  expaddzap  9669  expmulzap  9671  resqrtcl  10116  prmexpb  10737