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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 610 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∧ 𝜒) → (𝜓 ∧ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 |
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 396 |
This theorem is referenced by: mopick 2628 ssrmof 3990 rabss2 4015 lmcnp 22436 fbflim2 23109 ivthlem2 24597 ivthlem3 24598 arg-ax 34584 pm10.56 41941 |
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