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Theorem bnj1239 34345
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj1239 (∃𝑥𝐴 (𝜓𝜒) → ∃𝑥𝐴 𝜓)

Proof of Theorem bnj1239
StepHypRef Expression
1 simpl 482 . 2 ((𝜓𝜒) → 𝜓)
21reximi 3078 1 (∃𝑥𝐴 (𝜓𝜒) → ∃𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wrex 3064
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-rex 3065
This theorem is referenced by:  bnj1238  34346  bnj1299  34358  bnj66  34400
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