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Theorem bnj937 29889
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 1882 . 2 (∃𝑥𝜓𝜓)
31, 2sylib 206 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874
This theorem depends on definitions:  df-bi 195  df-ex 1695
This theorem is referenced by:  bnj1265  29930  bnj1379  29948  bnj852  30038  bnj1148  30111  bnj1154  30114  bnj1189  30124  bnj1245  30129  bnj1286  30134  bnj1311  30139  bnj1371  30144  bnj1374  30146  bnj1498  30176  bnj1514  30178
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