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Theorem bnj837 31138
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj837.1 (𝜂 ↔ (𝜑𝜓𝜒))
bnj837.2 (𝜒𝜏)
Assertion
Ref Expression
bnj837 (𝜂𝜏)

Proof of Theorem bnj837
StepHypRef Expression
1 bnj837.1 . 2 (𝜂 ↔ (𝜑𝜓𝜒))
2 bnj837.2 . . 3 (𝜒𝜏)
323ad2ant3 1130 . 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:  bnj1379  31208  bnj557  31278  bnj1175  31379  bnj1189  31384  bnj1417  31416
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