Theorem bj-hbsb3t 32712

Description: A theorem close to a closed form of hbsb3 2364. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-hbsb3t	|- ( A. x ( ph -> A. y ph ) -> ( [ y / x ] ph -> A. x [ y / x ] ph ) )

Proof of Theorem bj-hbsb3t

Step	Hyp	Ref	Expression
1		spsbim 2394	. 2 |- ( A. x ( ph -> A. y ph ) -> ( [ y / x ] ph -> [ y / x ] A. y ph ) )
2		hbsb2a 2361	. 2 |- ( [ y / x ] A. y ph -> A. x [ y / x ] ph )
3	1, 2	syl6 35	1 |- ( A. x ( ph -> A. y ph ) -> ( [ y / x ] ph -> A. x [ y / x ] ph ) )

Syntax hints:   -> wi 4   A.wal 1481   [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:  bj-hbsb3  32713  bj-nfs1t  32714