Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > alrimdOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of alrimd 2084 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
alrimdOLD.1 | ⊢ Ⅎ𝑥𝜑 |
alrimdOLD.2 | ⊢ Ⅎ𝑥𝜓 |
alrimdOLD.3 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
alrimdOLD | ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alrimdOLD.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | alrimdOLD.2 | . . 3 ⊢ Ⅎ𝑥𝜓 | |
3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝜓) |
4 | alrimdOLD.3 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
5 | 1, 3, 4 | alrimddOLD 2195 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1481 ℲwnfOLD 1709 |
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-12 2047 |
This theorem depends on definitions: df-bi 197 df-ex 1705 df-nfOLD 1721 |
This theorem is referenced by: nfimdOLD 2226 |
Copyright terms: Public domain | W3C validator |