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Mirrors > Home > MPE Home > Th. List > alrimddOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of alrimdd 2070 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
alrimddOLD.1 | ⊢ Ⅎ𝑥𝜑 |
alrimddOLD.2 | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
alrimddOLD.3 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
alrimddOLD | ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alrimddOLD.2 | . . 3 ⊢ (𝜑 → Ⅎ𝑥𝜓) | |
2 | 1 | nfrdOLD 2178 | . 2 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓)) |
3 | alrimddOLD.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
4 | alrimddOLD.3 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
5 | 3, 4 | alimdOLD 2179 | . 2 ⊢ (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒)) |
6 | 2, 5 | syld 46 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀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-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nfOLD 1712 |
This theorem is referenced by: alrimdOLD 2184 |
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