Theorem simpl3l 1057

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

Assertion

Ref	Expression
simpl3l	⊢ (((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏) → 𝜑)

Proof of Theorem simpl3l

Step	Hyp	Ref	Expression
1		simp3l 1030	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	adantr 276	1 ⊢ (((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏) → 𝜑)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 983

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 985

This theorem is referenced by:  tfisi  4656  ltmul1a  8706  ltmul1  8707  lemul1a  8973  xaddass  10033  swrdsbslen  11164  swrdspsleq  11165  dvdsadd2b  12317  dvdsaddre2b  12318  pockthg  12846