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Theorem bnj1254 34286
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1254.1 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
Assertion
Ref Expression
bnj1254 (𝜑𝜏)

Proof of Theorem bnj1254
StepHypRef Expression
1 bnj1254.1 . 2 (𝜑 ↔ (𝜓𝜒𝜃𝜏))
2 id 22 . . 3 (𝜏𝜏)
32bnj708 34233 . 2 ((𝜓𝜒𝜃𝜏) → 𝜏)
41, 3sylbi 216 1 (𝜑𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  w-bnj17 34163
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 206  df-an 396  df-bnj17 34164
This theorem is referenced by:  bnj554  34376  bnj557  34378  bnj967  34422  bnj999  34435  bnj907  34444  bnj1118  34461  bnj1128  34467  bnj1253  34494  bnj1450  34527
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