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Theorem bnj937 31174
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj937.1 (𝜑 → ∃𝑥𝜓)
Assertion
Ref Expression
bnj937 (𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem bnj937
StepHypRef Expression
1 bnj937.1 . 2 (𝜑 → ∃𝑥𝜓)
2 19.9v 2064 . 2 (∃𝑥𝜓𝜓)
31, 2sylib 208 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1851
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056
This theorem depends on definitions:  df-bi 197  df-ex 1852
This theorem is referenced by:  bnj1265  31215  bnj1379  31233  bnj852  31323  bnj1148  31396  bnj1154  31399  bnj1189  31409  bnj1245  31414  bnj1286  31419  bnj1311  31424  bnj1371  31429  bnj1374  31431  bnj1498  31461  bnj1514  31463
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