Theorem simpl3l 1083

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 1056	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) → 𝜑)
2	1	adantr 276	1 ⊢ (((𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜏) → 𝜑)

This proof depends on syntax axioms:   → wi 4   ∧ wa 104   ∧ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  tfisi  4734  ltmul1a  8920  ltmul1  8921  lemul1a  9189  xaddass  10273  swrdsbslen  11440  swrdspsleq  11441  dvdsadd2b  12609  dvdsaddre2b  12610  pockthg  13138