Theorem sbid2v 1343

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-17 971	. 2 |- (ph -> A.xph)
2	1	sbid2 1253	1 |- ([y / x][x / y]ph <-> ph)

Syntax hints:   <-> wb 146  [wsbc 1170

This theorem is referenced by:  sbelx 1344

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172

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