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Mirrors > Home > MPE Home > Th. List > pm3.45 | Structured version Visualization version GIF version |
Description: Theorem *3.45 (Fact) of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm3.45 | ⊢ ((𝜑 → 𝜓) → ((𝜑 ∧ 𝜒) → (𝜓 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓)) | |
2 | 1 | anim1d 612 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∧ 𝜒) → (𝜓 ∧ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 |
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 209 df-an 399 |
This theorem is referenced by: mopick 2710 ssrmof 4034 rabss2 4056 lmcnp 21914 fbflim2 22587 ivthlem2 24055 ivthlem3 24056 arg-ax 33766 pm10.56 40709 |
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