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Mirrors > Home > LLPE Home > Th. List > ax-send | Structured version |
Description: Message passing. |
Ref | Expression |
---|---|
ax-send | ⊦ (([z ≪ y] 𝜑 ⊗ [z ≫ x] 𝜓) ⊸ (𝜑 ⊗ [x ≔ y] 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . . 4 wff 𝜑 | |
2 | vz | . . . . 5 var z | |
3 | 2 | nvar 203 | . . . 4 nilad z |
4 | vy | . . . . 5 var y | |
5 | 4 | nvar 203 | . . . 4 nilad y |
6 | 1, 3, 5 | wse 204 | . . 3 wff [z ≪ y] 𝜑 |
7 | wps | . . . 4 wff 𝜓 | |
8 | vx | . . . 4 var x | |
9 | 7, 8, 3 | wre 205 | . . 3 wff [z ≫ x] 𝜓 |
10 | 6, 9 | wmc 105 | . 2 wff ([z ≪ y] 𝜑 ⊗ [z ≫ x] 𝜓) |
11 | 7, 8, 5 | wsub 207 | . . 3 wff [x ≔ y] 𝜓 |
12 | 1, 11 | wmc 105 | . 2 wff (𝜑 ⊗ [x ≔ y] 𝜓) |
13 | 10, 12 | wli 61 | 1 wff (([z ≪ y] 𝜑 ⊗ [z ≫ x] 𝜓) ⊸ (𝜑 ⊗ [x ≔ y] 𝜓)) |
Colors of variables: wff var nilad |
This axiom is referenced by: (None) |
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