![]() |
Mathbox for Jarvin Udandy |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > aisbnaxb | Structured version Visualization version GIF version |
Description: Given a is equivalent to b, there exists a proof for (not (a xor b)). (Contributed by Jarvin Udandy, 28-Aug-2016.) |
Ref | Expression |
---|---|
aisbnaxb.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
aisbnaxb | ⊢ ¬ (𝜑 ⊻ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aisbnaxb.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
2 | 1 | notnoti 136 | . 2 ⊢ ¬ ¬ (𝜑 ↔ 𝜓) |
3 | df-xor 1457 | . 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ¬ (𝜑 ↔ 𝜓)) | |
4 | 2, 3 | mtbir 312 | 1 ⊢ ¬ (𝜑 ⊻ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 195 ⊻ wxo 1456 |
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-xor 1457 |
This theorem is referenced by: dandysum2p2e4 39814 |
Copyright terms: Public domain | W3C validator |