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Theorem bj-cbvexivw 33166
Description: Change bound variable. This is to cbvexvw 2139 what cbvalivw 2106 is to cbvalvw 2138. [TODO: move after cbvalivw 2106]. (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 2008 . 2 (∃𝑥𝑦𝜓 → ∃𝑦𝜓)
2 ax-5 2006 . 2 (𝜑 → ∀𝑦𝜑)
3 bj-cbvexivw.1 . 2 (𝑦 = 𝑥 → (𝜑𝜓))
41, 2, 3bj-cbvexiw 33165 1 (∃𝑥𝜑 → ∃𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1875
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072
This theorem depends on definitions:  df-bi 199  df-ex 1876
This theorem is referenced by: (None)
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