Theorem bj-nfs1t 31308

Description: A theorem close to a closed form of nfs1 2193. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-nfs1t	|- ( A. x ( ph -> A. y ph ) -> F/ x [ y / x ] ph )

Proof of Theorem bj-nfs1t

Step	Hyp	Ref	Expression
1		bj-hbsb3t 31306	. . 3 |- ( A. x ( ph -> A. y ph ) -> ( [ y / x ] ph -> A. x [ y / x ] ph ) )
2	1	axc4i 1979	. 2 |- ( A. x ( ph -> A. y ph ) -> A. x ( [ y / x ] ph -> A. x [ y / x ] ph ) )
3		df-nf 1667	. 2 |- ( F/ x [ y / x ] ph <-> A. x ( [ y / x ] ph -> A. x [ y / x ] ph ) )
4	2, 3	sylibr 216	1 |- ( A. x ( ph -> A. y ph ) -> F/ x [ y / x ] ph )

Syntax hints:   -> wi 4   A.wal 1441   F/wnf 1666   [wsb 1796

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-12 1932  ax-13 2090

This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667  df-sb 1797

This theorem is referenced by:  bj-nfs1t2  31309