Metamath Proof Explorer


Theorem sbtrt

Description: Partially closed form of sbtr . Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by BJ, 4-Jun-2019) (New usage is discouraged.)

Ref Expression
Hypothesis sbtrt.nf
|- F/ y ph
Assertion sbtrt
|- ( A. y [ y / x ] ph -> ph )

Proof

Step Hyp Ref Expression
1 sbtrt.nf
 |-  F/ y ph
2 stdpc4
 |-  ( A. y [ y / x ] ph -> [ x / y ] [ y / x ] ph )
3 1 sbid2
 |-  ( [ x / y ] [ y / x ] ph <-> ph )
4 2 3 sylib
 |-  ( A. y [ y / x ] ph -> ph )