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Theorem bnj1247 29939
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1247.1 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
Assertion
Ref Expression
bnj1247 (𝜑𝜃)

Proof of Theorem bnj1247
StepHypRef Expression
1 bnj1247.1 . 2 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
2 id 22 . 2 (𝜃𝜃)
31, 2bnj771 29894 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  w-bnj17 29811
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 29812
This theorem is referenced by:  bnj1110  30110  bnj1128  30118  bnj1245  30142
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