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Theorem bnj769 29879
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 29870 . 2 ((𝜑𝜓𝜒𝜃) → 𝜏)
41, 3sylbi 205 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  w-bnj17 29798
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 195  df-an 384  df-3an 1032  df-bnj17 29799
This theorem is referenced by:  bnj966  30061  bnj967  30062  bnj986  30071  bnj1053  30091  bnj1030  30102  bnj1133  30104  bnj1450  30165
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