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Theorem simp321 1321
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp321 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)

Proof of Theorem simp321
StepHypRef Expression
1 simp21 1204 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜑)
213ad2ant3 1133 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1085
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 1087
This theorem is referenced by:  dalemcnes  38824  dalempnes  38825  dalemrot  38831  dath2  38911  cdleme18d  39469  cdleme20i  39491  cdleme20j  39492  cdleme20l2  39495  cdleme20l  39496  cdleme20m  39497  cdleme20  39498  cdleme21j  39510  cdleme22eALTN  39519  cdlemk16a  40030  cdlemk12u-2N  40064  cdlemk21-2N  40065  cdlemk22  40067  cdlemk31  40070  cdlemk32  40071  cdlemk11ta  40103  cdlemk11tc  40119
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