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Mirrors > Home > LLPE Home > Th. List > ax-almd | Structured version |
Description: Quantified multiplicative disjunction. This "distributes" a quantifier over linear implication. |
Ref | Expression |
---|---|
ax-almd | ⊦ (∀x(𝜑 ⊸ 𝜓) ⊸ (∀x𝜑 ⊸ ∀x𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . . 4 wff 𝜑 | |
2 | wps | . . . 4 wff 𝜓 | |
3 | 1, 2 | wli 61 | . . 3 wff (𝜑 ⊸ 𝜓) |
4 | vx | . . 3 var x | |
5 | 3, 4 | wal 318 | . 2 wff ∀x(𝜑 ⊸ 𝜓) |
6 | 1, 4 | wal 318 | . . 3 wff ∀x𝜑 |
7 | 2, 4 | wal 318 | . . 3 wff ∀x𝜓 |
8 | 6, 7 | wli 61 | . 2 wff (∀x𝜑 ⊸ ∀x𝜓) |
9 | 5, 8 | wli 61 | 1 wff (∀x(𝜑 ⊸ 𝜓) ⊸ (∀x𝜑 ⊸ ∀x𝜓)) |
Colors of variables: wff var nilad |
This axiom is referenced by: (None) |
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