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Theorem bnj835 34604
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 1130 . 2 ((𝜑𝜓𝜒) → 𝜏)
41, 3sylbi 216 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  w3a 1084
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 395  df-3an 1086
This theorem is referenced by:  bnj1219  34645  bnj1379  34675  bnj1175  34849  bnj1286  34864  bnj1280  34865  bnj1296  34866  bnj1398  34879  bnj1415  34883  bnj1417  34886  bnj1421  34887  bnj1442  34894  bnj1450  34895  bnj1452  34897  bnj1489  34901  bnj1312  34903  bnj1501  34912  bnj1523  34916
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