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Mirrors > Home > ILE Home > Th. List > orbi1 | GIF version |
Description: Theorem *4.37 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
orbi1 | ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓)) | |
2 | 1 | orbi1d 737 | 1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 103 ∨ wo 661 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: prmdvdsexp 10527 |
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