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Theorem simprr1 1029
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simprr1 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)

Proof of Theorem simprr1
StepHypRef Expression
1 simpr1 987 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜑)
21adantl 275 1 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 962
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 964
This theorem is referenced by:  icodiamlt  10959  summodc  11159  prodmodc  11354
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