Metamath Proof Explorer


Definition df-hmph

Description: Definition of the relation x is homeomorphic to y . (Contributed by FL, 14-Feb-2007)

Ref Expression
Assertion df-hmph ≃ = ( ◡ Homeo “ ( V ∖ 1o ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 chmph ⊢ ≃
1 chmeo ⊢ Homeo
2 1 ccnv ⊢ ◡ Homeo
3 cvv ⊢ V
4 c1o ⊢ 1o
5 3 4 cdif ⊢ ( V ∖ 1o )
6 2 5 cima ⊢ ( ◡ Homeo “ ( V ∖ 1o ) )
7 0 6 wceq ⊢ ≃ = ( ◡ Homeo “ ( V ∖ 1o ) )