Theorem sbidd-misc 42460

Description: An identity theorem for substitution. See sbid 2114. See Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017.)

Assertion

Ref	Expression
sbidd-misc	|- ( ( ph -> [ x / x ] ps ) <-> ( ph -> ps ) )

Proof of Theorem sbidd-misc

Step	Hyp	Ref	Expression
1		sbid 2114	. 2 |- ( [ x / x ] ps <-> ps )
2	1	imbi2i 326	1 |- ( ( ph -> [ x / x ] ps ) <-> ( ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 196   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-sb 1881

This theorem is referenced by: (None)