A ⊃ A {\displaystyle A\supset A}
1. A ⊃ ( A ⊃ A ) {\displaystyle 1.\,\,A\supset \left({A\supset A}\right)}
// աքսիոմ 1 ( A = A , B = A {\displaystyle A=A,\,\,B=A} )
2. ( A ⊃ ( A ⊃ A ) ) ⊃ ( ( A ⊃ ( ( A ⊃ A ) ⊃ A ) ) ⊃ ( A ⊃ A ) ) {\displaystyle 2.\,\,\left({A\supset \left({A\supset A}\right)}\right)\supset \left({\left({A\supset \left({\left({A\supset A}\right)\supset A}\right)}\right)\supset \left({A\supset A}\right)}\right)}
// աքսիոմ 2 ( A = A , B = ( A ⊃ A ) , C = A {\displaystyle A=A,\,\,B=\left({A\supset A}\right),\,\,C=A} )
3. ( A ⊃ ( ( A ⊃ A ) ⊃ A ) ) ⊃ ( A ⊃ A ) {\displaystyle 3.\,\,\left({A\supset \left({\left({A\supset A}\right)\supset A}\right)}\right)\supset \left({A\supset A}\right)}
// m.p. (1,2)
4. A ⊃ ( ( A ⊃ A ) ⊃ A ) {\displaystyle 4.\,\,A\supset \left({\left({A\supset A}\right)\supset A}\right)}
// աքսիոմ 1 ( A = A , B = ( A ⊃ A ) {\displaystyle A=A,\,\,B=\left({A\supset A}\right)} )
5. A ⊃ A {\displaystyle 5.\,\,A\supset A}
// m.p. (3,4)
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