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Theorem simplr3 983
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simplr3 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜒)

Proof of Theorem simplr3
StepHypRef Expression
1 simpr3 947 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
21adantr 270 1 (((𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜏) → 𝜒)
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:  prarloclemlt  6954  prarloclemlo  6955  resqrexlemdecn  10271
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