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Theorem bnj1266 29938
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1266.1 (𝜒 → ∃𝑥(𝜑𝜓))
Assertion
Ref Expression
bnj1266 (𝜒 → ∃𝑥𝜓)

Proof of Theorem bnj1266
StepHypRef Expression
1 bnj1266.1 . 2 (𝜒 → ∃𝑥(𝜑𝜓))
2 simpr 475 . 2 ((𝜑𝜓) → 𝜓)
31, 2bnj593 29871 1 (𝜒 → ∃𝑥𝜓)
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 1711  ax-4 1726
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695
This theorem is referenced by:  bnj1265  29939
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