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Theorem bnj832 31156
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj832.1 (𝜂 ↔ (𝜑𝜓))
bnj832.2 (𝜑𝜏)
Assertion
Ref Expression
bnj832 (𝜂𝜏)

Proof of Theorem bnj832
StepHypRef Expression
1 bnj832.1 . 2 (𝜂 ↔ (𝜑𝜓))
2 bnj832.2 . . 3 (𝜑𝜏)
32adantr 472 . 2 ((𝜑𝜓) → 𝜏)
41, 3sylbi 207 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383
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
This theorem is referenced by:  bnj1379  31229  bnj605  31305  bnj908  31329  bnj1145  31389  bnj1442  31445  bnj1450  31446  bnj1489  31452  bnj1501  31463  bnj1523  31467
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