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Theorem bnj835 31136
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 1128 . 2 ((𝜑𝜓𝜒) → 𝜏)
41, 3sylbi 207 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w3a 1072
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 197  df-an 385  df-3an 1074
This theorem is referenced by:  bnj1219  31178  bnj1379  31208  bnj1175  31379  bnj1286  31394  bnj1280  31395  bnj1296  31396  bnj1398  31409  bnj1415  31413  bnj1417  31416  bnj1421  31417  bnj1442  31424  bnj1450  31425  bnj1452  31427  bnj1489  31431  bnj1312  31433  bnj1501  31442  bnj1523  31446
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