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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-cbv3hv2 | Structured version Visualization version GIF version |
Description: Version of cbv3h 2404 with two disjoint variable conditions, which does not require ax-11 2162 nor ax-13 2372. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-cbv3hv2.nf | ⊢ (𝜓 → ∀𝑥𝜓) |
bj-cbv3hv2.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
bj-cbv3hv2 | ⊢ (∀𝑥𝜑 → ∀𝑦𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-cbv3hv2.nf | . . 3 ⊢ (𝜓 → ∀𝑥𝜓) | |
2 | 1 | nf5i 2150 | . 2 ⊢ Ⅎ𝑥𝜓 |
3 | bj-cbv3hv2.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
4 | 2, 3 | cbv3v2 2243 | 1 ⊢ (∀𝑥𝜑 → ∀𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-10 2145 ax-12 2179 |
This theorem depends on definitions: df-bi 210 df-ex 1787 df-nf 1791 |
This theorem is referenced by: (None) |
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