Theorem sbid2v 1382

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]ph <-> ph)

Distinct variable group:   ph,x

Proof of Theorem sbid2v

Step	Hyp	Ref	Expression
1		ax-17 1007	. 2 |- (ph -> A.xph)
2	1	sbid2 1291	1 |- ([y / x][x / y]ph <-> ph)

Syntax hints:   <-> wb 144  [wsbc 1207

This theorem is referenced by:  sbelx 1383

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 998  ax-gen 999  ax-8 1000  ax-10 1002  ax-12 1004  ax-17 1007  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159  ax-10o 1177  ax-11o 1255

This theorem depends on definitions:  df-bi 145  df-or 222  df-an 223  df-ex 1017  df-sb 1209

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