Metamath Proof Explorer


Theorem aisfbistiaxb

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 ( 𝜑𝜓 )

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 ( 𝜑𝜓 )