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Theorem bnj835 34752
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 1132 . 2 ((𝜑𝜓𝜒) → 𝜏)
41, 3sylbi 217 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 206  w3a 1086
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 207  df-an 396  df-3an 1088
This theorem is referenced by:  bnj1219  34793  bnj1379  34823  bnj1175  34997  bnj1286  35012  bnj1280  35013  bnj1296  35014  bnj1398  35027  bnj1415  35031  bnj1417  35034  bnj1421  35035  bnj1442  35042  bnj1450  35043  bnj1452  35045  bnj1489  35049  bnj1312  35051  bnj1501  35060  bnj1523  35064
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