Metamath Proof Explorer


Theorem sbidd

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

Ref Expression
Hypothesis sbidd.1
|- ( ph -> [ x / x ] ps )
Assertion sbidd
|- ( ph -> ps )

Proof

Step Hyp Ref Expression
1 sbidd.1
 |-  ( ph -> [ x / x ] ps )
2 sbid
 |-  ( [ x / x ] ps <-> ps )
3 1 2 sylib
 |-  ( ph -> ps )