Theorem sbid 1221

Description: An identity theorem for substitution. Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint).

Assertion

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

Proof of Theorem sbid

Step	Hyp	Ref	Expression
1		equid 1162	. . 3 |- x = x
2		sbequ12 1218	. . 3 |- (x = x -> (ph <-> [x / x]ph))
3	1, 2	ax-mp 7	. 2 |- (ph <-> [x / x]ph)
4	3	bicomi 170	1 |- ([x / x]ph <-> ph)

Syntax hints:   <-> wb 144  [wsbc 1207

This theorem is referenced by:  abid 1507  sbceq1a 1989  csbid 2056

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 999  ax-12 1004  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159

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

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