Description: Equality theorem for the range Cartesian product, inference form. (Contributed by Peter Mazsa, 16-Dec-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | xrneq1i.1 | ⊢ 𝐴 = 𝐵 | |
Assertion | xrneq1i | ⊢ ( 𝐴 ⋉ 𝐶 ) = ( 𝐵 ⋉ 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xrneq1i.1 | ⊢ 𝐴 = 𝐵 | |
2 | xrneq1 | ⊢ ( 𝐴 = 𝐵 → ( 𝐴 ⋉ 𝐶 ) = ( 𝐵 ⋉ 𝐶 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐴 ⋉ 𝐶 ) = ( 𝐵 ⋉ 𝐶 ) |