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Theorem bnj1299 29945
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1299.1 (𝜑 → ∃𝑥𝐴 (𝜓𝜒))
Assertion
Ref Expression
bnj1299 (𝜑 → ∃𝑥𝐴 𝜓)

Proof of Theorem bnj1299
StepHypRef Expression
1 bnj1299.1 . 2 (𝜑 → ∃𝑥𝐴 (𝜓𝜒))
2 bnj1239 29932 . 2 (∃𝑥𝐴 (𝜓𝜒) → ∃𝑥𝐴 𝜓)
31, 2syl 17 1 (𝜑 → ∃𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wrex 2892
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695  df-ral 2896  df-rex 2897
This theorem is referenced by:  bnj1497  30184  bnj1498  30185  bnj1501  30191
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