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Theorem bnj835 33801
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj835.1 (𝜂 ↔ (𝜑𝜓𝜒))
bnj835.2 (𝜑𝜏)
Assertion
Ref Expression
bnj835 (𝜂𝜏)

Proof of Theorem bnj835
StepHypRef Expression
1 bnj835.1 . 2 (𝜂 ↔ (𝜑𝜓𝜒))
2 bnj835.2 . . 3 (𝜑𝜏)
323ad2ant1 1134 . 2 ((𝜑𝜓𝜒) → 𝜏)
41, 3sylbi 216 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  w3a 1088
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 398  df-3an 1090
This theorem is referenced by:  bnj1219  33842  bnj1379  33872  bnj1175  34046  bnj1286  34061  bnj1280  34062  bnj1296  34063  bnj1398  34076  bnj1415  34080  bnj1417  34083  bnj1421  34084  bnj1442  34091  bnj1450  34092  bnj1452  34094  bnj1489  34098  bnj1312  34100  bnj1501  34109  bnj1523  34113
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