![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > alrimd | Structured version Visualization version GIF version |
Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 2195. (Contributed by Mario Carneiro, 24-Sep-2016.) |
Ref | Expression |
---|---|
alrimd.1 | ⊢ Ⅎ𝑥𝜑 |
alrimd.2 | ⊢ Ⅎ𝑥𝜓 |
alrimd.3 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
alrimd | ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alrimd.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | alrimd.2 | . . 3 ⊢ Ⅎ𝑥𝜓 | |
3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝜓) |
4 | alrimd.3 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
5 | 1, 3, 4 | alrimdd 2202 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1531 Ⅎwnf 1777 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-12 2166 |
This theorem depends on definitions: df-bi 206 df-ex 1774 df-nf 1778 |
This theorem is referenced by: moexexlem 2617 ralrimd 3259 pssnn 9199 pssnnOLD 9296 fiint 9356 wl-mo3t 37076 pm14.24 43900 |
Copyright terms: Public domain | W3C validator |