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Theorem bnj1239 32085
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 485 . 2 ((𝜓𝜒) → 𝜓)
21reximi 3230 1 (∃𝑥𝐴 (𝜓𝜒) → ∃𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  wrex 3126
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781  df-ral 3130  df-rex 3131
This theorem is referenced by:  bnj1238  32086  bnj1299  32098  bnj66  32140
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