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Mirrors > Home > LLPE Home > Th. List > mdm1 | Structured version |
Description: Par is monotone in its first argument. |
Ref | Expression |
---|---|
mdm1.1 | ⊦ (𝜃 ⅋ (𝜑 ⅋ 𝜓)) |
mdm1.2 | ⊦ (𝜑 ⊸ 𝜒) |
Ref | Expression |
---|---|
mdm1 | ⊦ (𝜃 ⅋ (𝜒 ⅋ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mdm1.1 | . . . 4 ⊦ (𝜃 ⅋ (𝜑 ⅋ 𝜓)) | |
2 | 1 | mdcod 11 | . . 3 ⊦ (𝜃 ⅋ (𝜓 ⅋ 𝜑)) |
3 | mdm1.2 | . . 3 ⊦ (𝜑 ⊸ 𝜒) | |
4 | 2, 3 | mdm2 69 | . 2 ⊦ (𝜃 ⅋ (𝜓 ⅋ 𝜒)) |
5 | 4 | mdcod 11 | 1 ⊦ (𝜃 ⅋ (𝜒 ⅋ 𝜓)) |
Colors of variables: wff var nilad |
Syntax hints: ⅋ wmd 2 ⊸ wli 61 |
This theorem was proved from axioms: ax-ibot 4 ax-ebot 5 ax-cut 6 ax-init 7 ax-mdco 8 ax-mdas 9 ax-eac1 33 |
This theorem depends on definitions: df-lb 56 df-li 62 |
This theorem is referenced by: mdm1i 71 mdm1s 73 |
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