Theorem simpl2l 1053

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simpl2l	⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Proof of Theorem simpl2l

Step	Hyp	Ref	Expression
1		simp2l 1026	. 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) → 𝜑)
2	1	adantr 276	1 ⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 981

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 983

This theorem is referenced by:  xaddass  9998  swrdsbslen  11127  swrdspsleq  11128  xrbdtri  11631  pockthg  12724