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Theorem bnj937 31942
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 1979 . 2 (∃𝑥𝜓𝜓)
31, 2sylib 219 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961
This theorem depends on definitions:  df-bi 208  df-ex 1772
This theorem is referenced by:  bnj1265  31983  bnj1379  32001  bnj852  32092  bnj1148  32165  bnj1154  32168  bnj1189  32178  bnj1245  32183  bnj1286  32188  bnj1311  32193  bnj1371  32198  bnj1374  32200  bnj1498  32230  bnj1514  32232
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