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| Mirrors > Home > LLPE Home > Th. List > ax-subre1 | Structured version | |
| Ref | Expression |
|---|---|
| ax-subre1 | ⊦ ([x ≔ y] [x ≫ a] 𝜑 ⧟ [x ≔ y] [y ≫ a] 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wph | . . . 4 wff 𝜑 | |
| 2 | va | . . . 4 var a | |
| 3 | vx | . . . . 5 var x | |
| 4 | 3 | nvar 203 | . . . 4 nilad x |
| 5 | 1, 2, 4 | wre 205 | . . 3 wff [x ≫ a] 𝜑 |
| 6 | vy | . . . 4 var y | |
| 7 | 6 | nvar 203 | . . 3 nilad y |
| 8 | 5, 3, 7 | wsub 207 | . 2 wff [x ≔ y] [x ≫ a] 𝜑 |
| 9 | 1, 2, 7 | wre 205 | . . 3 wff [y ≫ a] 𝜑 |
| 10 | 9, 3, 7 | wsub 207 | . 2 wff [x ≔ y] [y ≫ a] 𝜑 |
| 11 | 8, 10 | wlb 55 | 1 wff ([x ≔ y] [x ≫ a] 𝜑 ⧟ [x ≔ y] [y ≫ a] 𝜑) |
| Colors of variables: wff var nilad |
| This axiom is referenced by: (None) |
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