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Theorem simpl3l 1052
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpl3l (((𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜏) → 𝜑)

Proof of Theorem simpl3l
StepHypRef Expression
1 simp3l 1025 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜑)
21adantr 276 1 (((𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜏) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 978
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 980
This theorem is referenced by:  tfisi  4588  ltmul1a  8550  ltmul1  8551  lemul1a  8817  xaddass  9871  dvdsadd2b  11849  dvdsaddre2b  11850  pockthg  12357
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