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Mirrors > Home > MPE Home > Th. List > pm4.83 | Structured version Visualization version GIF version |
Description: Theorem *4.83 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm4.83 | ⊢ (((𝜑 → 𝜓) ∧ (¬ 𝜑 → 𝜓)) ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmid 892 | . . 3 ⊢ (𝜑 ∨ ¬ 𝜑) | |
2 | 1 | a1bi 363 | . 2 ⊢ (𝜓 ↔ ((𝜑 ∨ ¬ 𝜑) → 𝜓)) |
3 | jaob 959 | . 2 ⊢ (((𝜑 ∨ ¬ 𝜑) → 𝜓) ↔ ((𝜑 → 𝜓) ∧ (¬ 𝜑 → 𝜓))) | |
4 | 2, 3 | bitr2i 275 | 1 ⊢ (((𝜑 → 𝜓) ∧ (¬ 𝜑 → 𝜓)) ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 205 ∧ wa 396 ∨ wo 844 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 |
This theorem is referenced by: cases2 1045 dmdbr5ati 30784 cvlsupr3 37358 rp-fakeanorass 41120 |
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