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Mirrors > Home > MPE Home > Th. List > Mathboxes > uun121 | 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 |
---|---|
uun121.1 | ⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) → 𝜒) |
Ref | Expression |
---|---|
uun121 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anabs5 847 | . 2 ⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) ↔ (𝜑 ∧ 𝜓)) | |
2 | uun121.1 | . 2 ⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) → 𝜒) | |
3 | 1, 2 | sylbir 224 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
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 196 df-an 385 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |