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Mirrors > Home > MPE Home > Th. List > pm4.42 | Structured version Visualization version GIF version |
Description: Theorem *4.42 of [WhiteheadRussell] p. 119. See also ifpid 1019. (Contributed by Roy F. Longton, 21-Jun-2005.) |
Ref | Expression |
---|---|
pm4.42 | ⊢ (𝜑 ↔ ((𝜑 ∧ 𝜓) ∨ (𝜑 ∧ ¬ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dedlema 993 | . 2 ⊢ (𝜓 → (𝜑 ↔ ((𝜑 ∧ 𝜓) ∨ (𝜑 ∧ ¬ 𝜓)))) | |
2 | dedlemb 994 | . 2 ⊢ (¬ 𝜓 → (𝜑 ↔ ((𝜑 ∧ 𝜓) ∨ (𝜑 ∧ ¬ 𝜓)))) | |
3 | 1, 2 | pm2.61i 175 | 1 ⊢ (𝜑 ↔ ((𝜑 ∧ 𝜓) ∨ (𝜑 ∧ ¬ 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 195 ∨ wo 382 ∧ wa 383 |
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 196 df-or 384 df-an 385 |
This theorem is referenced by: inundif 3998 numclwwlk3lem 26635 elim2ifim 28748 smatrcl 29190 expdioph 36608 av-numclwwlk3lem 41538 |
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