Metamath Proof Explorer

Theorem nfich2

Description: The second interchangeable setvar variable is not free. (Contributed by AV, 21-Aug-2023)

Ref Expression
Assertion nfich2 
|- F/ y [ x <> y ] ph

Proof

Step Hyp Ref Expression
1 df-ich 
 |-  ( [ x <> y ] ph <-> A. x A. y ( [ x / a ] [ y / x ] [ a / y ] ph <-> ph ) )
2 nfa2 
 |-  F/ y A. x A. y ( [ x / a ] [ y / x ] [ a / y ] ph <-> ph )
3 1 2 nfxfr 
 |-  F/ y [ x <> y ] ph