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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-dvv | Structured version Visualization version GIF version |
Description: A special instance of bj-hbaeb2 32805. A lemma for distinct var metavariables. Note that the right-hand side is a closed formula (a sentence). (Contributed by BJ, 6-Oct-2018.) |
Ref | Expression |
---|---|
bj-dvv | ⊢ (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥∀𝑦 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-hbaeb2 32805 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥∀𝑦 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: ↔ 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 ax-7 1935 ax-10 2019 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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