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Mirrors > Home > MPE Home > Th. List > 19.21-2OLD | Structured version Visualization version GIF version |
Description: Obsolete proof of 19.21-2 2065 as of 6-Oct-2021. (Contributed by NM, 4-Feb-2005.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
19.21-2OLD.1 | ⊢ Ⅎ𝑥𝜑 |
19.21-2OLD.2 | ⊢ Ⅎ𝑦𝜑 |
Ref | Expression |
---|---|
19.21-2OLD | ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) ↔ (𝜑 → ∀𝑥∀𝑦𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.21-2OLD.2 | . . . 4 ⊢ Ⅎ𝑦𝜑 | |
2 | 1 | 19.21OLD 2202 | . . 3 ⊢ (∀𝑦(𝜑 → 𝜓) ↔ (𝜑 → ∀𝑦𝜓)) |
3 | 2 | albii 1737 | . 2 ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) ↔ ∀𝑥(𝜑 → ∀𝑦𝜓)) |
4 | 19.21-2OLD.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
5 | 4 | 19.21OLD 2202 | . 2 ⊢ (∀𝑥(𝜑 → ∀𝑦𝜓) ↔ (𝜑 → ∀𝑥∀𝑦𝜓)) |
6 | 3, 5 | bitri 263 | 1 ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) ↔ (𝜑 → ∀𝑥∀𝑦𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 195 ∀wal 1473 ℲwnfOLD 1700 |
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 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nfOLD 1712 |
This theorem is referenced by: (None) |
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