Theorem ex-pr

Description: Example for df-pr . (Contributed by Mario Carneiro, 7-May-2015)

	Ref	Expression
Assertion	ex-pr	⊢ ( 𝐴 ∈ { 1 , - 1 } → ( 𝐴 ↑ 2 ) = 1 )

Proof

Step	Hyp	Ref	Expression
1		elpri	⊢ ( 𝐴 ∈ { 1 , - 1 } → ( 𝐴 = 1 ∨ 𝐴 = - 1 ) )
2		oveq1	⊢ ( 𝐴 = 1 → ( 𝐴 ↑ 2 ) = ( 1 ↑ 2 ) )
3		sq1	⊢ ( 1 ↑ 2 ) = 1
4	2 3	eqtrdi	⊢ ( 𝐴 = 1 → ( 𝐴 ↑ 2 ) = 1 )
5		oveq1	⊢ ( 𝐴 = - 1 → ( 𝐴 ↑ 2 ) = ( - 1 ↑ 2 ) )
6		neg1sqe1	⊢ ( - 1 ↑ 2 ) = 1
7	5 6	eqtrdi	⊢ ( 𝐴 = - 1 → ( 𝐴 ↑ 2 ) = 1 )
8	4 7	jaoi	⊢ ( ( 𝐴 = 1 ∨ 𝐴 = - 1 ) → ( 𝐴 ↑ 2 ) = 1 )
9	1 8	syl	⊢ ( 𝐴 ∈ { 1 , - 1 } → ( 𝐴 ↑ 2 ) = 1 )