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Theorem bnj937 30096
 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 1883 . 2 (∃𝑥𝜓𝜓)
31, 2sylib 207 1 (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1695 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875 This theorem depends on definitions:  df-bi 196  df-ex 1696 This theorem is referenced by:  bnj1265  30137  bnj1379  30155  bnj852  30245  bnj1148  30318  bnj1154  30321  bnj1189  30331  bnj1245  30336  bnj1286  30341  bnj1311  30346  bnj1371  30351  bnj1374  30353  bnj1498  30383  bnj1514  30385
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