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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-cbvexivw | Structured version Visualization version GIF version |
Description: Change bound variable. This is to cbvexvw 1957 what cbvalivw 1921 is to cbvalvw 1956. [TODO: move after cbvalivw 1921]. (Contributed by BJ, 17-Mar-2020.) |
Ref | Expression |
---|---|
bj-cbvexivw.1 | ⊢ (𝑦 = 𝑥 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
bj-cbvexivw | ⊢ (∃𝑥𝜑 → ∃𝑦𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax5e 1829 | . 2 ⊢ (∃𝑥∃𝑦𝜓 → ∃𝑦𝜓) | |
2 | ax-5 1827 | . 2 ⊢ (𝜑 → ∀𝑦𝜑) | |
3 | bj-cbvexivw.1 | . 2 ⊢ (𝑦 = 𝑥 → (𝜑 → 𝜓)) | |
4 | 1, 2, 3 | bj-cbvexiw 31846 | 1 ⊢ (∃𝑥𝜑 → ∃𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1695 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 |
This theorem depends on definitions: df-bi 196 df-ex 1696 |
This theorem is referenced by: (None) |
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