Theorem sbtrt 2420

Description: Partially closed form of sbtr 2421. (Contributed by BJ, 4-Jun-2019.)

Hypothesis

Ref	Expression
sbtrt.nf	|- F/ y ph

Assertion

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

Proof of Theorem sbtrt

Step	Hyp	Ref	Expression
1		stdpc4 2353	. 2 |- ( A. y [ y / x ] ph -> [ x / y ] [ y / x ] ph )
2		sbtrt.nf	. . 3 |- F/ y ph
3	2	sbid2 2413	. 2 |- ( [ x / y ] [ y / x ] ph <-> ph )
4	1, 3	sylib 208	1 |- ( A. y [ y / x ] ph -> ph )

Syntax hints:   -> wi 4   A.wal 1481   F/wnf 1708   [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-10 2019  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-sb 1881

This theorem is referenced by:  sbtr  2421