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Theorem bnj1235 30129
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1235.1 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
Assertion
Ref Expression
bnj1235 (𝜑𝜒)

Proof of Theorem bnj1235
StepHypRef Expression
1 bnj1235.1 . 2 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
2 id 22 . 2 (𝜒𝜒)
31, 2bnj770 30087 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  w-bnj17 30005
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 196  df-an 385  df-3an 1033  df-bnj17 30006
This theorem is referenced by:  bnj966  30268  bnj967  30269  bnj910  30272  bnj1006  30283  bnj1018  30286  bnj1110  30304  bnj1121  30307  bnj1311  30346
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