Description: An equality deduction for the subclass relationship. (Contributed by NM, 14-Aug-1994)
Ref | Expression | ||
---|---|---|---|
Hypothesis | sseq1d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
Assertion | sseq2d | ⊢ ( 𝜑 → ( 𝐶 ⊆ 𝐴 ↔ 𝐶 ⊆ 𝐵 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | sseq2 | ⊢ ( 𝐴 = 𝐵 → ( 𝐶 ⊆ 𝐴 ↔ 𝐶 ⊆ 𝐵 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 𝐶 ⊆ 𝐴 ↔ 𝐶 ⊆ 𝐵 ) ) |