Theorem sbid2v 2123

Description: An identity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint). (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
sbid2v	⊢ ([y / x][x / y]φ ↔ φ)

Distinct variable group:   φ,x

Allowed substitution hint:   φ(y)

Proof of Theorem sbid2v

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxφ
2	1	sbid2 2084	1 ⊢ ([y / x][x / y]φ ↔ φ)

Syntax hints:   ↔ wb 176  [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:  sbelx  2124