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Mirrors > Home > MPE Home > Th. List > pm5.31 | Structured version Visualization version GIF version |
Description: Theorem *5.31 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm5.31 | ⊢ ((𝜒 ∧ (𝜑 → 𝜓)) → (𝜑 → (𝜓 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.21 464 | . . 3 ⊢ (𝜒 → (𝜓 → (𝜓 ∧ 𝜒))) | |
2 | 1 | imim2d 57 | . 2 ⊢ (𝜒 → ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜒)))) |
3 | 2 | imp 445 | 1 ⊢ ((𝜒 ∧ (𝜑 → 𝜓)) → (𝜑 → (𝜓 ∧ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 |
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 197 df-an 386 |
This theorem is referenced by: bj-bary1lem1 33161 |
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