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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-cbv3v2 | Structured version Visualization version GIF version |
Description: Version of cbv3 2265 with two dv conditions, which does not require ax-11 2034 nor ax-13 2246. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-cbv3v2.nf | ⊢ Ⅎ𝑥𝜓 |
bj-cbv3v2.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
bj-cbv3v2 | ⊢ (∀𝑥𝜑 → ∀𝑦𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . 2 ⊢ Ⅎ𝑦∀𝑥𝜑 | |
2 | bj-cbv3v2.nf | . . 3 ⊢ Ⅎ𝑥𝜓 | |
3 | bj-cbv3v2.1 | . . 3 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
4 | 2, 3 | spimv1 2115 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) |
5 | 1, 4 | alrimi 2082 | 1 ⊢ (∀𝑥𝜑 → ∀𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1481 Ⅎwnf 1708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-ex 1705 df-nf 1710 |
This theorem is referenced by: bj-cbv3hv2 32728 |
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