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Mirrors > Home > ILE Home > Th. List > pm4.77 | GIF version |
Description: Theorem *4.77 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm4.77 | ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) ↔ ((𝜓 ∨ 𝜒) → 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jaob 631 | . 2 ⊢ (((𝜓 ∨ 𝜒) → 𝜑) ↔ ((𝜓 → 𝜑) ∧ (𝜒 → 𝜑))) | |
2 | 1 | bicomi 123 | 1 ⊢ (((𝜓 → 𝜑) ∧ (𝜒 → 𝜑)) ↔ ((𝜓 ∨ 𝜒) → 𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ↔ wb 98 ∨ wo 629 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: (None) |
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