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Theorem simp332 1324
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp332 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜓)

Proof of Theorem simp332
StepHypRef Expression
1 simp32 1207 . 2 ((𝜃𝜏 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant3 1132 1 ((𝜂𝜁 ∧ (𝜃𝜏 ∧ (𝜑𝜓𝜒))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1084
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 206  df-an 395  df-3an 1086
This theorem is referenced by:  ivthALT  35852  dalemclqjt  39140  dath2  39242  cdlema1N  39296  cdleme26eALTN  39866  cdlemk7u  40375  cdlemk11u  40376  cdlemk12u  40377  cdlemk23-3  40407  cdlemk33N  40414  cdlemk11ta  40434  cdlemk11tc  40450  cdlemk54  40463
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