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Theorem bnj1235 31182
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 31140 1 (𝜑𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w-bnj17 31061
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 385  df-3an 1074  df-bnj17 31062
This theorem is referenced by:  bnj966  31321  bnj967  31322  bnj910  31325  bnj1006  31336  bnj1018  31339  bnj1110  31357  bnj1121  31360  bnj1311  31399
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