Theorem a9e 809

Description: At least one individual exists.

Assertion

Ref	Expression
a9e	⊢ ∃x x = y

Proof of Theorem a9e

Step	Hyp	Ref	Expression
1		ax9a 808	. 2 ⊢ ¬ ∀x ¬ x = y
2		df-ex 679	. 2 ⊢ (∃x x = y ↔ ¬ ∀x ¬ x = y)
3	1, 2	mpbir 165	1 ⊢ ∃x x = y

Syntax hints:  ¬ wn 1  ∀wal 672  ∃wex 678   = weq 797

This theorem is referenced by:  eqvin.l1 851  zfext2 1087  zfaus 1480  opabsb 2114  dmi 2545  1st2val 3097  ecelqsi 3229  axextnd 3737

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-9 799

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

metamath.org