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Mirrors > Home > MPE Home > Th. List > Mathboxes > hbra2VD | Structured version Visualization version GIF version |
Description: Virtual deduction proof of nfra2 2930. The following user's proof is
completed by invoking mmj2's unify command and using mmj2's
StepSelector to pick all remaining steps of the Metamath proof.
|
Ref | Expression |
---|---|
hbra2VD | ⊢ (∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 → ∀𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralcom 3079 | . 2 ⊢ (∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 ↔ ∀𝑦 ∈ 𝐵 ∀𝑥 ∈ 𝐴 𝜑) | |
2 | hbra1 2926 | . 2 ⊢ (∀𝑦 ∈ 𝐵 ∀𝑥 ∈ 𝐴 𝜑 → ∀𝑦∀𝑦 ∈ 𝐵 ∀𝑥 ∈ 𝐴 𝜑) | |
3 | 1, 2 | hbxfrbi 1742 | 1 ⊢ (∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 → ∀𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 ∀wral 2896 |
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-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ral 2901 |
This theorem is referenced by: (None) |
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