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Mirrors > Home > MPE Home > Th. List > Mathboxes > aistbisfiaxb | Structured version Visualization version GIF version |
Description: Given a is equivalent to T., Given b is equivalent to F. there exists a proof for a-xor-b. (Contributed by Jarvin Udandy, 31-Aug-2016.) |
Ref | Expression |
---|---|
aistbisfiaxb.1 | ⊢ (𝜑 ↔ ⊤) |
aistbisfiaxb.2 | ⊢ (𝜓 ↔ ⊥) |
Ref | Expression |
---|---|
aistbisfiaxb | ⊢ (𝜑 ⊻ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aistbisfiaxb.1 | . . 3 ⊢ (𝜑 ↔ ⊤) | |
2 | 1 | aistia 43915 | . 2 ⊢ 𝜑 |
3 | aistbisfiaxb.2 | . . 3 ⊢ (𝜓 ↔ ⊥) | |
4 | 3 | aisfina 43916 | . 2 ⊢ ¬ 𝜓 |
5 | 2, 4 | abnotbtaxb 43933 | 1 ⊢ (𝜑 ⊻ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ⊻ wxo 1506 ⊤wtru 1543 ⊥wfal 1554 |
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 210 df-an 400 df-xor 1507 df-tru 1545 df-fal 1555 |
This theorem is referenced by: (None) |
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