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Theorem bnj534 29865
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj534.1 (𝜒 → (∃𝑥𝜑𝜓))
Assertion
Ref Expression
bnj534 (𝜒 → ∃𝑥(𝜑𝜓))
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜒(𝑥)

Proof of Theorem bnj534
StepHypRef Expression
1 bnj534.1 . 2 (𝜒 → (∃𝑥𝜑𝜓))
2 19.41v 1900 . 2 (∃𝑥(𝜑𝜓) ↔ (∃𝑥𝜑𝜓))
31, 2sylibr 222 1 (𝜒 → ∃𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wex 1694
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695
This theorem is referenced by:  bnj600  30046  bnj852  30048
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