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Theorem bnj1232 31000
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 30944 . 2 ((𝜓𝜒𝜃𝜏) → 𝜓)
31, 2sylbi 207 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w-bnj17 30880
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 1056  df-bnj17 30881
This theorem is referenced by:  bnj605  31103  bnj607  31112  bnj944  31134  bnj969  31142  bnj970  31143  bnj1001  31154  bnj1110  31176  bnj1118  31178  bnj1128  31184  bnj1145  31187  bnj1311  31218
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