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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 31993. 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 31993 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥∀𝑦 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ∀wal 1473 |
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-10 2006 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 |
This theorem is referenced by: (None) |
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