Theorem bj-nfs1t2 32715

Description: A theorem close to a closed form of nfs1 2365. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-nfs1t2	|- ( A. x F/ y ph -> F/ x [ y / x ] ph )

Proof of Theorem bj-nfs1t2

Step	Hyp	Ref	Expression
1		nf5r 2064	. . 3 |- ( F/ y ph -> ( ph -> A. y ph ) )
2	1	alimi 1739	. 2 |- ( A. x F/ y ph -> A. x ( ph -> A. y ph ) )
3		bj-nfs1t 32714	. 2 |- ( A. x ( ph -> A. y ph ) -> F/ x [ y / x ] ph )
4	2, 3	syl 17	1 |- ( A. x F/ y ph -> F/ x [ y / x ] 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:  bj-nfs1  32716