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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-spvv | Structured version Visualization version GIF version |
Description: Version of spv 2260 with a dv condition, which does not require ax-7 1935, ax-12 2047, ax-13 2246. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-spvv.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
bj-spvv | ⊢ (∀𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-spvv.1 | . . 3 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
2 | 1 | biimpd 219 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
3 | 2 | bj-spimvv 32721 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 ∀wal 1481 |
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 |
This theorem depends on definitions: df-bi 197 df-ex 1705 |
This theorem is referenced by: bj-chvarvv 32726 bj-nalset 32794 bj-ru0 32932 |
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