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Theorem bnj836 29878
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj836.1 (𝜂 ↔ (𝜑𝜓𝜒))
bnj836.2 (𝜓𝜏)
Assertion
Ref Expression
bnj836 (𝜂𝜏)

Proof of Theorem bnj836
StepHypRef Expression
1 bnj836.1 . 2 (𝜂 ↔ (𝜑𝜓𝜒))
2 bnj836.2 . . 3 (𝜓𝜏)
323ad2ant2 1076 . 2 ((𝜑𝜓𝜒) → 𝜏)
41, 3sylbi 206 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  w3a 1031
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 196  df-an 385  df-3an 1033
This theorem is referenced by:  bnj1379  29949  bnj1175  30120  bnj1286  30135  bnj1450  30166  bnj1501  30183  bnj1523  30187
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