Theorem sbid2 1804

Description: An identity law for substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.)

Hypothesis

Ref	Expression
sbid2.1	|- F/ x ph

Assertion

Ref	Expression
sbid2	|- ( [ y / x ] [ x / y ] ph <-> ph )

Proof of Theorem sbid2

Step	Hyp	Ref	Expression
1		sbid2.1	. . 3 |- F/ x ph
2	1	nfri 1482	. 2 |- ( ph -> A. x ph )
3	2	sbid2h 1803	1 |- ( [ y / x ] [ x / y ] ph <-> ph )

Syntax hints:   <-> wb 104   F/wnf 1419   [wsb 1718

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497

This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719

This theorem is referenced by:  sbco4lem  1957