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Theorem bnj1239 31204
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 474 . 2 ((𝜓𝜒) → 𝜓)
21reximi 3149 1 (∃𝑥𝐴 (𝜓𝜒) → ∃𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wrex 3051
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-ral 3055  df-rex 3056
This theorem is referenced by:  bnj1238  31205  bnj1299  31217  bnj66  31258
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