Theorem sbid2 2084

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/xph

Assertion

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

Proof of Theorem sbid2

Step	Hyp	Ref	Expression
1		sbco 2083	. 2 |- ([y / x][x / y]ph <-> [y / x]ph)
2		sbid2.1	. . 3 |- F/xph
3	2	sbf 2026	. 2 |- ([y / x]ph <-> ph)
4	1, 3	bitri 240	1 |- ([y / x][x / y]ph <-> ph)

Syntax hints:   <-> wb 176   F/wnf 1544  [wsb 1648

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  df-sb 1649

This theorem is referenced by:  sbco2  2086  sb5rf  2090  sb6rf  2091  sbid2v  2123