Theorem bj-ssbid1ALT 32648

Description: Alternate proof of bj-ssbid1 32647, not using bj-ssbequ1 32644. (Contributed by BJ, 22-Dec-2020.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
bj-ssbid1ALT	|- ( ph -> [ x/ x]b ph )

Proof of Theorem bj-ssbid1ALT

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ax12v 2048	. . . . 5 |- ( x = y -> ( ph -> A. x ( x = y -> ph ) ) )
2	1	equcoms 1947	. . . 4 |- ( y = x -> ( ph -> A. x ( x = y -> ph ) ) )
3	2	com12 32	. . 3 |- ( ph -> ( y = x -> A. x ( x = y -> ph ) ) )
4	3	alrimiv 1855	. 2 |- ( ph -> A. y ( y = x -> A. x ( x = y -> ph ) ) )
5		df-ssb 32620	. 2 |- ([ x/ x]b ph <-> A. y ( y = x -> A. x ( x = y -> ph ) ) )
6	4, 5	sylibr 224	1 |- ( ph -> [ x/ x]b ph )

Syntax hints:   -> wi 4   A.wal 1481  [wssb 32619

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-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-ssb 32620

This theorem is referenced by: (None)