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Mirrors > Home > MPE Home > Th. List > anc2r | Structured version Visualization version GIF version |
Description: Conjoin antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) |
Ref | Expression |
---|---|
anc2r | ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → (𝜒 ∧ 𝜑)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.21 471 | . . 3 ⊢ (𝜑 → (𝜒 → (𝜒 ∧ 𝜑))) | |
2 | 1 | imim2d 57 | . 2 ⊢ (𝜑 → ((𝜓 → 𝜒) → (𝜓 → (𝜒 ∧ 𝜑)))) |
3 | 2 | a2i 14 | 1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → (𝜒 ∧ 𝜑)))) |
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: ssorduni 7619 |
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