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Mirrors > Home > ILE Home > Th. List > pm5.44 | GIF version |
Description: Theorem *5.44 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm5.44 | ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) ↔ (𝜑 → (𝜓 ∧ 𝜒)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jcab 593 | . 2 ⊢ ((𝜑 → (𝜓 ∧ 𝜒)) ↔ ((𝜑 → 𝜓) ∧ (𝜑 → 𝜒))) | |
2 | 1 | baibr 906 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) ↔ (𝜑 → (𝜓 ∧ 𝜒)))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ↔ wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: reldisj 3445 |
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