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Theorem simp3rl 1059
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3rl ((𝜃𝜏 ∧ (𝜒 ∧ (𝜑𝜓))) → 𝜑)

Proof of Theorem simp3rl
StepHypRef Expression
1 simprl 521 . 2 ((𝜒 ∧ (𝜑𝜓)) → 𝜑)
213ad2ant3 1009 1 ((𝜃𝜏 ∧ (𝜒 ∧ (𝜑𝜓))) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 967
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 969
This theorem is referenced by:  prarloc  7438  tgqioo  13145
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