Mathbox for Giovanni Mascellani |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > tsan2 | Structured version Visualization version GIF version |
Description: A Tseitin axiom for logical conjunction, in deduction form. (Contributed by Giovanni Mascellani, 24-Mar-2018.) |
Ref | Expression |
---|---|
tsan2 | ⊢ (𝜃 → (𝜑 ∨ ¬ (𝜑 ∧ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.14 522 | . . . 4 ⊢ ((¬ 𝜑 ∨ ¬ 𝜓) → ¬ (𝜑 ∧ 𝜓)) | |
2 | 1 | orcs 408 | . . 3 ⊢ (¬ 𝜑 → ¬ (𝜑 ∧ 𝜓)) |
3 | 2 | orri 390 | . 2 ⊢ (𝜑 ∨ ¬ (𝜑 ∧ 𝜓)) |
4 | 3 | a1i 11 | 1 ⊢ (𝜃 → (𝜑 ∨ ¬ (𝜑 ∧ 𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 382 ∧ 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-or 384 df-an 385 |
This theorem is referenced by: tsna2 33122 ts3an2 33128 mpt2bi123f 33141 mptbi12f 33145 |
Copyright terms: Public domain | W3C validator |