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Theorem nfeqf 1958
Description: A variable is effectively not free in an equality if it is not either of the involved variables.  F/ version of ax-12o 2142. (Contributed by Mario Carneiro, 6-Oct-2016.)
Assertion
Ref Expression
nfeqf  F/

Proof of Theorem nfeqf
StepHypRef Expression
1 nfnae 1956 . . 3  F/
2 nfnae 1956 . . 3  F/
31, 2nfan 1824 . 2  F/
4 ax12o 1934 . . 3
54imp 418 . 2
63, 5nfd 1766 1  F/
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wa 358  wal 1540   F/wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  equvini  1987  equveli  1988  nfsb4t  2080  sbcom  2089  nfeud2  2216
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