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Theorem bnj1131 31196
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1131.1 (𝜑 → ∀𝑥𝜑)
bnj1131.2 𝑥𝜑
Assertion
Ref Expression
bnj1131 𝜑

Proof of Theorem bnj1131
StepHypRef Expression
1 bnj1131.2 . 2 𝑥𝜑
2 bnj1131.1 . . 3 (𝜑 → ∀𝑥𝜑)
3219.9h 2283 . 2 (∃𝑥𝜑𝜑)
41, 3mpbi 220 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1629  wex 1852
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-10 2174  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-ex 1853  df-nf 1858
This theorem is referenced by:  bnj1468  31254  bnj1014  31368  bnj1128  31396
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