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Theorem bnj769 31932
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj769.1 (𝜂 ↔ (𝜑𝜓𝜒𝜃))
bnj769.2 (𝜑𝜏)
Assertion
Ref Expression
bnj769 (𝜂𝜏)

Proof of Theorem bnj769
StepHypRef Expression
1 bnj769.1 . 2 (𝜂 ↔ (𝜑𝜓𝜒𝜃))
2 bnj769.2 . . 3 (𝜑𝜏)
32bnj705 31923 . 2 ((𝜑𝜓𝜒𝜃) → 𝜏)
41, 3sylbi 218 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  w-bnj17 31855
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 208  df-an 397  df-3an 1081  df-bnj17 31856
This theorem is referenced by:  bnj966  32115  bnj967  32116  bnj986  32125  bnj1053  32145  bnj1030  32156  bnj1133  32158  bnj1450  32219
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