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Theorem bnj1247 32767
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 32723 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  w-bnj17 32644
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 206  df-an 396  df-3an 1087  df-bnj17 32645
This theorem is referenced by:  bnj1110  32941  bnj1128  32949  bnj1245  32973
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