Description: Equality theorem for the range Cartesian product, deduction form. (Contributed by Peter Mazsa, 7-Sep-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | xrneq2d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
Assertion | xrneq2d | ⊢ ( 𝜑 → ( 𝐶 ⋉ 𝐴 ) = ( 𝐶 ⋉ 𝐵 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xrneq2d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | xrneq2 | ⊢ ( 𝐴 = 𝐵 → ( 𝐶 ⋉ 𝐴 ) = ( 𝐶 ⋉ 𝐵 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 𝐶 ⋉ 𝐴 ) = ( 𝐶 ⋉ 𝐵 ) ) |