Metamath Proof Explorer
Description: Given a is equivalent to F., Given b is equivalent to T., there exists a
proof for a-xor-b. (Contributed by Jarvin Udandy, 31-Aug-2016)
|
|
Ref |
Expression |
|
Hypotheses |
aisfbistiaxb.1 |
⊢ ( 𝜑 ↔ ⊥ ) |
|
|
aisfbistiaxb.2 |
⊢ ( 𝜓 ↔ ⊤ ) |
|
Assertion |
aisfbistiaxb |
⊢ ( 𝜑 ⊻ 𝜓 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
aisfbistiaxb.1 |
⊢ ( 𝜑 ↔ ⊥ ) |
2 |
|
aisfbistiaxb.2 |
⊢ ( 𝜓 ↔ ⊤ ) |
3 |
1
|
aisfina |
⊢ ¬ 𝜑 |
4 |
2
|
aistia |
⊢ 𝜓 |
5 |
3 4
|
abnotataxb |
⊢ ( 𝜑 ⊻ 𝜓 ) |