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Metamath Proof Explorer

Theorem nfcnv

Description: Bound-variable hypothesis builder for converse relation. (Contributed by NM, 31-Jan-2004) (Revised by Mario Carneiro, 15-Oct-2016)

Ref Expression
Hypothesis nfcnv.1 ⊢ Ⅎ _ x A
Assertion nfcnv ⊢ Ⅎ _ x A -1

Proof

Step Hyp Ref Expression
1 nfcnv.1 ⊢ Ⅎ _ x A
2 df-cnv ⊢ A -1 = y z | z A y
3 nfcv ⊢ Ⅎ _ x z
4 nfcv ⊢ Ⅎ _ x y
5 3 1 4 nfbr ⊢ Ⅎ x z A y
6 5 nfopab ⊢ Ⅎ _ x y z | z A y
7 2 6 nfcxfr ⊢ Ⅎ _ x A -1