Theorem equequ1OLD 1685

Description: Obsolete version of equequ1 1684 as of 12-Nov-2017. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
equequ1OLD	⊢ (x = y → (x = z ↔ y = z))

Proof of Theorem equequ1OLD

Step	Hyp	Ref	Expression
1		ax-8 1675	. 2 ⊢ (x = y → (x = z → y = z))
2		equcomi 1679	. . 3 ⊢ (x = y → y = x)
3		ax-8 1675	. . 3 ⊢ (y = x → (y = z → x = z))
4	2, 3	syl 15	. 2 ⊢ (x = y → (y = z → x = z))
5	1, 4	impbid 183	1 ⊢ (x = y → (x = z ↔ y = z))

Syntax hints:   → wi 4   ↔ wb 176

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 depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by: (None)