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Theorem simpl3l 994
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 967 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜑)
21adantr 270 1 (((𝜒𝜃 ∧ (𝜑𝜓)) ∧ 𝜏) → 𝜑)
Colors of variables: wff set class
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:  tfisi  4356  ltmul1a  7828  ltmul1  7829  lemul1a  8073  dvdsadd2b  10468
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