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Mirrors > Home > MPE Home > Th. List > Mathboxes > 3anidm12p2 | Structured version Visualization version GIF version |
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
3anidm12p2.1 | ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜑) → 𝜒) |
Ref | Expression |
---|---|
3anidm12p2 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anrot 1101 | . . 3 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜑) ↔ (𝜑 ∧ 𝜑 ∧ 𝜓)) | |
2 | 3anidm12p2.1 | . . 3 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜑) → 𝜒) | |
3 | 1, 2 | sylbir 238 | . 2 ⊢ ((𝜑 ∧ 𝜑 ∧ 𝜓) → 𝜒) |
4 | 3 | 3anidm12 1420 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∧ w3a 1088 |
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 210 df-an 400 df-3an 1090 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |