Theorem wl-id 33265

Description: Principle of identity. Theorem *2.08 of [WhiteheadRussell] p. 101. Copy of id 22 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
wl-id	|- ( ph -> ph )

Proof of Theorem wl-id

Step	Hyp	Ref	Expression
1		ax-luk3 33243	. 2 |- ( ph -> ( -. ph -> ph ) )
2		ax-luk2 33242	. 2 |- ( ( -. ph -> ph ) -> ph )
3	1, 2	wl-syl 33246	1 |- ( ph -> ph )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 33241  ax-luk2 33242  ax-luk3 33243

This theorem is referenced by:  wl-notnotr  33266