Theorem equidOLD 1677

Description: Obsolete proof of equid 1676 as of 9-Dec-2017. (Contributed by NM, 1-Apr-2005.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equidOLD	⊢ x = x

Proof of Theorem equidOLD

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ax9v 1655	. . 3 ⊢ ¬ ∀y ¬ y = x
2		ax-8 1675	. . . . . 6 ⊢ (y = x → (y = x → x = x))
3	2	pm2.43i 43	. . . . 5 ⊢ (y = x → x = x)
4	3	con3i 127	. . . 4 ⊢ (¬ x = x → ¬ y = x)
5	4	alimi 1559	. . 3 ⊢ (∀y ¬ x = x → ∀y ¬ y = x)
6	1, 5	mto 167	. 2 ⊢ ¬ ∀y ¬ x = x
7		ax-17 1616	. 2 ⊢ (¬ x = x → ∀y ¬ x = x)
8	6, 7	mt3 171	1 ⊢ x = x

Syntax hints:  ¬ wn 3  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675

This theorem is referenced by: (None)