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Metamath Proof Explorer

Theorem ideq

Description: For sets, the identity relation is the same as equality. (Contributed by NM, 13-Aug-1995)

Ref Expression
Hypothesis ideq.1 ⊢ B ∈ V
Assertion ideq ⊢ A I B ↔ A = B

Proof

Step Hyp Ref Expression
1 ideq.1 ⊢ B ∈ V
2 ideqg ⊢ B ∈ V → A I B ↔ A = B
3 1 2 ax-mp ⊢ A I B ↔ A = B