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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-dvdemo2 | Structured version Visualization version GIF version |
Description: Remove dependency on ax-13 2234 from dvdemo2 4830 (this removal is noteworthy since dvdemo1 4829 and dvdemo2 4830 illustrate the phenomenon of bundling). (Contributed by BJ, 16-Jul-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-dvdemo2 | ⊢ ∃𝑥(𝑥 = 𝑦 → 𝑧 ∈ 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-el 31984 | . 2 ⊢ ∃𝑥 𝑧 ∈ 𝑥 | |
2 | ax-1 6 | . 2 ⊢ (𝑧 ∈ 𝑥 → (𝑥 = 𝑦 → 𝑧 ∈ 𝑥)) | |
3 | 1, 2 | eximii 1754 | 1 ⊢ ∃𝑥(𝑥 = 𝑦 → 𝑧 ∈ 𝑥) |
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 ax-7 1922 ax-8 1979 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-pow 4769 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 df-nf 1701 |
This theorem is referenced by: (None) |
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