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Theorem bnj1232 31974
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1232.1 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
Assertion
Ref Expression
bnj1232 (𝜑𝜓)

Proof of Theorem bnj1232
StepHypRef Expression
1 bnj1232.1 . 2 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
2 bnj642 31918 . 2 ((𝜓𝜒𝜃𝜏) → 𝜓)
31, 2sylbi 218 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  w-bnj17 31855
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 208  df-an 397  df-3an 1081  df-bnj17 31856
This theorem is referenced by:  bnj605  32078  bnj607  32087  bnj944  32109  bnj969  32117  bnj970  32118  bnj1001  32129  bnj1110  32151  bnj1118  32153  bnj1128  32159  bnj1145  32162  bnj1311  32193
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