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Theorem bnj937 33513
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 1987 . 2 (∃𝑥𝜓𝜓)
31, 2sylib 217 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971
This theorem depends on definitions:  df-bi 206  df-ex 1782
This theorem is referenced by:  bnj1265  33554  bnj1379  33572  bnj852  33663  bnj1148  33738  bnj1154  33741  bnj1189  33751  bnj1245  33756  bnj1286  33761  bnj1311  33766  bnj1371  33771  bnj1374  33773  bnj1498  33803  bnj1514  33805
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