Theorem a8b 817

Description: An equivalence law for equality.

Assertion

Ref	Expression
a8b	⊢ (x = y → (x = z ↔ y = z))

Proof of Theorem a8b

Step	Hyp	Ref	Expression
1		ax-8 798	. 2 ⊢ (x = y → (x = z → y = z))
2		eqt 814	. 2 ⊢ (x = y → (y = z → x = z))
3	1, 2	impbid 397	1 ⊢ (x = y → (x = z ↔ y = z))

Syntax hints:   → wi 2   ↔ wb 127   = weq 797

This theorem is referenced by:  ddeeq1 1001  sb8eu 1017  axac 1085  zfext2 1087  aceq0 3553  axrepndlem1 3738  axpowndlem2 3744  axacndlem5 3757  zfcndac 3765

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-8 798  ax-9 799  ax-12 802

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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