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Metamath Proof Explorer

Theorem cbviinvg

Description: Change bound variables in an indexed intersection. Usage of this theorem is discouraged because it depends on ax-13 . Usage of the weaker cbviinv is preferred. (Contributed by Jeff Hankins, 26-Aug-2009) (New usage is discouraged.)

Ref Expression
Hypothesis cbviunvg.1 ⊢ x = y → B = C
Assertion cbviinvg ⊢ ⋂ x ∈ A B = ⋂ y ∈ A C

Proof

Step Hyp Ref Expression
1 cbviunvg.1 ⊢ x = y → B = C
2 nfcv ⊢ Ⅎ _ y B
3 nfcv ⊢ Ⅎ _ x C
4 2 3 1 cbviing ⊢ ⋂ x ∈ A B = ⋂ y ∈ A C