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Theorem bj-cbvexivw 34090
 Description: Change bound variable. This is to cbvexvw 2045 what cbvalivw 2015 is to cbvalvw 2044. TODO: move after cbvalivw 2015. (Contributed by BJ, 17-Mar-2020.)
Hypothesis
Ref Expression
bj-cbvexivw.1 (𝑦 = 𝑥 → (𝜑𝜓))
Assertion
Ref Expression
bj-cbvexivw (∃𝑥𝜑 → ∃𝑦𝜓)
Distinct variable groups:   𝑥,𝑦   𝜓,𝑥   𝜑,𝑦
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem bj-cbvexivw
StepHypRef Expression
1 ax5e 1914 . 2 (∃𝑥𝑦𝜓 → ∃𝑦𝜓)
2 ax-5 1912 . 2 (𝜑 → ∀𝑦𝜑)
3 bj-cbvexivw.1 . 2 (𝑦 = 𝑥 → (𝜑𝜓))
41, 2, 3bj-cbvexiw 34089 1 (∃𝑥𝜑 → ∃𝑦𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1781 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971 This theorem depends on definitions:  df-bi 210  df-ex 1782 This theorem is referenced by: (None)
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