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Mirrors > Home > MPE Home > Th. List > Mathboxes > un10 | Structured version Visualization version GIF version |
Description: A unionizing deduction. (Contributed by Alan Sare, 28-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
un10.1 | ⊢ ( ( 𝜑 , ⊤ ) ▶ 𝜓 ) |
Ref | Expression |
---|---|
un10 | ⊢ ( 𝜑 ▶ 𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1543 | . . . 4 ⊢ ⊤ | |
2 | 1 | jctr 525 | . . 3 ⊢ (𝜑 → (𝜑 ∧ ⊤)) |
3 | un10.1 | . . . 4 ⊢ ( ( 𝜑 , ⊤ ) ▶ 𝜓 ) | |
4 | 3 | dfvd2ani 42203 | . . 3 ⊢ ((𝜑 ∧ ⊤) → 𝜓) |
5 | 2, 4 | syl 17 | . 2 ⊢ (𝜑 → 𝜓) |
6 | 5 | dfvd1ir 42193 | 1 ⊢ ( 𝜑 ▶ 𝜓 ) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 396 ⊤wtru 1540 ( wvd1 42189 ( wvhc2 42200 |
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 397 df-tru 1542 df-vd1 42190 df-vhc2 42201 |
This theorem is referenced by: (None) |
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