Theorem sbid2v 993

Description: An identity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint).

Assertion

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

Distinct variable group(s):   φ,x

Proof of Theorem sbid2v

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (φ → ∀xφ)
2	1	sbid2 911	1 ⊢ ([y / x][x / y]φ ↔ φ)

Syntax hints:   ↔ wb 127  [wsb 852

This theorem is referenced by:  sbelx 994

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853

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