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Mirrors > Home > MPE Home > Th. List > eqsstri | Structured version Visualization version GIF version |
Description: Substitution of equality into a subclass relationship. (Contributed by NM, 16-Jul-1995.) |
Ref | Expression |
---|---|
eqsstr.1 | ⊢ 𝐴 = 𝐵 |
eqsstr.2 | ⊢ 𝐵 ⊆ 𝐶 |
Ref | Expression |
---|---|
eqsstri | ⊢ 𝐴 ⊆ 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqsstr.2 | . 2 ⊢ 𝐵 ⊆ 𝐶 | |
2 | eqsstr.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
3 | 2 | sseq1i 3929 | . 2 ⊢ (𝐴 ⊆ 𝐶 ↔ 𝐵 ⊆ 𝐶) |
4 | 1, 3 | mpbir 234 | 1 ⊢ 𝐴 ⊆ 𝐶 |
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