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Mirrors > Home > ILE Home > Th. List > orim2d | GIF version |
Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.) |
Ref | Expression |
---|---|
orim1d.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
orim2d | ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idd 21 | . 2 ⊢ (𝜑 → (𝜃 → 𝜃)) | |
2 | orim1d.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
3 | 1, 2 | orim12d 738 | 1 ⊢ (𝜑 → ((𝜃 ∨ 𝜓) → (𝜃 ∨ 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 667 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: orim2 741 orbi2d 742 pm2.82 764 pm2.13dc 820 stabtestimpdc 865 acexmidlemcase 5685 poxp 6035 fodjuomnilemdc 6887 indpi 6998 nneoor 8947 uzp1 9151 maxabslemlub 10771 xrmaxiflemlub 10807 bj-nn0suc 12571 |
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