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Theorem bnj1238 30131
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1238.1 (𝜑 ↔ ∃𝑥𝐴 (𝜓𝜒))
Assertion
Ref Expression
bnj1238 (𝜑 → ∃𝑥𝐴 𝜓)

Proof of Theorem bnj1238
StepHypRef Expression
1 bnj1238.1 . 2 (𝜑 ↔ ∃𝑥𝐴 (𝜓𝜒))
2 bnj1239 30130 . 2 (∃𝑥𝐴 (𝜓𝜒) → ∃𝑥𝐴 𝜓)
31, 2sylbi 206 1 (𝜑 → ∃𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  wa 383  wrex 2897
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-ral 2901  df-rex 2902
This theorem is referenced by:  bnj1245  30336  bnj1256  30337  bnj1259  30338  bnj1311  30346  bnj1371  30351
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