Description: The restricted converse epsilon coset of an element of the restriction is the element itself. (Contributed by Peter Mazsa, 16-Jul-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | eccnvepres2 | ⊢ ( 𝐵 ∈ 𝐴 → [ 𝐵 ] ( ◡ E ↾ 𝐴 ) = 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecres2 | ⊢ ( 𝐵 ∈ 𝐴 → [ 𝐵 ] ( ◡ E ↾ 𝐴 ) = [ 𝐵 ] ◡ E ) | |
2 | eccnvep | ⊢ ( 𝐵 ∈ 𝐴 → [ 𝐵 ] ◡ E = 𝐵 ) | |
3 | 1 2 | eqtrd | ⊢ ( 𝐵 ∈ 𝐴 → [ 𝐵 ] ( ◡ E ↾ 𝐴 ) = 𝐵 ) |