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Mirrors > Home > LLPE Home > Th. List > df-im | Structured version |
Description: Definition of →. It's ⊸ but with some ! splashed in for good measure. Note that only 𝜑 needs the exponential. When this statement is beneath a ! or at the top level, this is equivalent to both sides having the exponential, because of |
Ref | Expression |
---|---|
df-im | ⊦ ((𝜑 → 𝜓) ⧟ (! 𝜑 ⊸ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff 𝜑 | |
2 | wps | . . 3 wff 𝜓 | |
3 | 1, 2 | wim 180 | . 2 wff (𝜑 → 𝜓) |
4 | 1 | wpe 148 | . . 3 wff ! 𝜑 |
5 | 4, 2 | wli 61 | . 2 wff (! 𝜑 ⊸ 𝜓) |
6 | 3, 5 | wlb 55 | 1 wff ((𝜑 → 𝜓) ⧟ (! 𝜑 ⊸ 𝜓)) |
Colors of variables: wff var nilad |
This definition is referenced by: (None) |
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