Description: Equality deduction for conditional operator. (Contributed by NM, 16-Feb-2005)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ifeq1d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
Assertion | ifeq2d | ⊢ ( 𝜑 → if ( 𝜓 , 𝐶 , 𝐴 ) = if ( 𝜓 , 𝐶 , 𝐵 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifeq1d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | ifeq2 | ⊢ ( 𝐴 = 𝐵 → if ( 𝜓 , 𝐶 , 𝐴 ) = if ( 𝜓 , 𝐶 , 𝐵 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → if ( 𝜓 , 𝐶 , 𝐴 ) = if ( 𝜓 , 𝐶 , 𝐵 ) ) |