![]() |
Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > simplbi2comtVD | Structured version Visualization version GIF version |
Description: Virtual deduction proof of simplbi2comt 500.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
simplbi2comt 500 is simplbi2comtVD 43953 without virtual deductions and was
automatically derived from simplbi2comtVD 43953.
|
Ref | Expression |
---|---|
simplbi2comtVD | ⊢ ((𝜑 ↔ (𝜓 ∧ 𝜒)) → (𝜒 → (𝜓 → 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idn1 43639 | . . . . 5 ⊢ ( (𝜑 ↔ (𝜓 ∧ 𝜒)) ▶ (𝜑 ↔ (𝜓 ∧ 𝜒)) ) | |
2 | biimpr 219 | . . . . 5 ⊢ ((𝜑 ↔ (𝜓 ∧ 𝜒)) → ((𝜓 ∧ 𝜒) → 𝜑)) | |
3 | 1, 2 | e1a 43692 | . . . 4 ⊢ ( (𝜑 ↔ (𝜓 ∧ 𝜒)) ▶ ((𝜓 ∧ 𝜒) → 𝜑) ) |
4 | pm3.3 447 | . . . 4 ⊢ (((𝜓 ∧ 𝜒) → 𝜑) → (𝜓 → (𝜒 → 𝜑))) | |
5 | 3, 4 | e1a 43692 | . . 3 ⊢ ( (𝜑 ↔ (𝜓 ∧ 𝜒)) ▶ (𝜓 → (𝜒 → 𝜑)) ) |
6 | pm2.04 90 | . . 3 ⊢ ((𝜓 → (𝜒 → 𝜑)) → (𝜒 → (𝜓 → 𝜑))) | |
7 | 5, 6 | e1a 43692 | . 2 ⊢ ( (𝜑 ↔ (𝜓 ∧ 𝜒)) ▶ (𝜒 → (𝜓 → 𝜑)) ) |
8 | 7 | in1 43636 | 1 ⊢ ((𝜑 ↔ (𝜓 ∧ 𝜒)) → (𝜒 → (𝜓 → 𝜑))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∧ wa 394 |
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 395 df-vd1 43635 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |