Detailed syntax breakdown of Axiom ax-4oa
| Step | Hyp | Ref
| Expression |
|---|
| 1 | | wva |
. . . 4
term a |
| 2 | | wvd |
. . . 4
term d |
| 3 | 1, 2 | wi1 12 |
. . 3
term (a →1 d) |
| 4 | | wvb |
. . . . . 6
term b |
| 5 | 1, 4 | wa 7 |
. . . . 5
term (a ∩ b) |
| 6 | 4, 2 | wi1 12 |
. . . . . 6
term (b →1 d) |
| 7 | 3, 6 | wa 7 |
. . . . 5
term ((a →1 d) ∩ (b
→1 d)) |
| 8 | 5, 7 | wo 6 |
. . . 4
term ((a ∩ b) ∪
((a →1 d) ∩ (b
→1 d))) |
| 9 | | wvc |
. . . . . . 7
term c |
| 10 | 1, 9 | wa 7 |
. . . . . 6
term (a ∩ c) |
| 11 | 9, 2 | wi1 12 |
. . . . . . 7
term (c →1 d) |
| 12 | 3, 11 | wa 7 |
. . . . . 6
term ((a →1 d) ∩ (c
→1 d)) |
| 13 | 10, 12 | wo 6 |
. . . . 5
term ((a ∩ c) ∪
((a →1 d) ∩ (c
→1 d))) |
| 14 | 4, 9 | wa 7 |
. . . . . 6
term (b ∩ c) |
| 15 | 6, 11 | wa 7 |
. . . . . 6
term ((b →1 d) ∩ (c
→1 d)) |
| 16 | 14, 15 | wo 6 |
. . . . 5
term ((b ∩ c) ∪
((b →1 d) ∩ (c
→1 d))) |
| 17 | 13, 16 | wa 7 |
. . . 4
term (((a ∩ c) ∪
((a →1 d) ∩ (c
→1 d))) ∩ ((b ∩ c) ∪
((b →1 d) ∩ (c
→1 d)))) |
| 18 | 8, 17 | wo 6 |
. . 3
term (((a ∩ b) ∪
((a →1 d) ∩ (b
→1 d))) ∪ (((a ∩ c) ∪
((a →1 d) ∩ (c
→1 d))) ∩ ((b ∩ c) ∪
((b →1 d) ∩ (c
→1 d))))) |
| 19 | 3, 18 | wa 7 |
. 2
term ((a →1 d) ∩ (((a
∩ b) ∪ ((a →1 d) ∩ (b
→1 d))) ∪ (((a ∩ c) ∪
((a →1 d) ∩ (c
→1 d))) ∩ ((b ∩ c) ∪
((b →1 d) ∩ (c
→1 d)))))) |
| 20 | 19, 6 | wle 2 |
1
wff ((a →1 d) ∩ (((a
∩ b) ∪ ((a →1 d) ∩ (b
→1 d))) ∪ (((a ∩ c) ∪
((a →1 d) ∩ (c
→1 d))) ∩ ((b ∩ c) ∪
((b →1 d) ∩ (c
→1 d)))))) ≤ (b →1 d) |
