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Theorem bnj1232 29922
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 29866 . 2 ((𝜓𝜒𝜃𝜏) → 𝜓)
31, 2sylbi 206 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  w-bnj17 29799
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 29800
This theorem is referenced by:  bnj605  30025  bnj607  30034  bnj944  30056  bnj969  30064  bnj970  30065  bnj1001  30076  bnj1110  30098  bnj1118  30100  bnj1128  30106  bnj1145  30109  bnj1311  30140
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