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Theorem bnj771 31169
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj771.1 (𝜂 ↔ (𝜑𝜓𝜒𝜃))
bnj771.2 (𝜒𝜏)
Assertion
Ref Expression
bnj771 (𝜂𝜏)

Proof of Theorem bnj771
StepHypRef Expression
1 bnj771.1 . 2 (𝜂 ↔ (𝜑𝜓𝜒𝜃))
2 bnj771.2 . . 3 (𝜒𝜏)
32bnj707 31160 . 2 ((𝜑𝜓𝜒𝜃) → 𝜏)
41, 3sylbi 207 1 (𝜂𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w-bnj17 31089
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 383  df-3an 1073  df-bnj17 31090
This theorem is referenced by:  bnj1247  31214  bnj996  31360  bnj1097  31384  bnj1145  31396  bnj1259  31419  bnj1296  31424  bnj1450  31453
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