Theorem sbid2 1874

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 1543	. 2 |- ( ph -> A. x ph )
3	2	sbid2h 1873	1 |- ( [ y / x ] [ x / y ] ph <-> ph )

Syntax hints:   <-> wb 105   F/wnf 1484   [wsb 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787

This theorem is referenced by:  sbco4lem  2035