Metamath Proof Explorer

Theorem ax6ev

Description: At least one individual exists. Weaker version of ax6e . When possible, use of this theorem rather than ax6e is preferred since its derivation is much shorter and requires fewer axioms. (Contributed by NM, 3-Aug-2017)

Ref Expression
Assertion ax6ev x x = y


Step Hyp Ref Expression
1 ax6v ¬ x ¬ x = y
2 df-ex x x = y ¬ x ¬ x = y
3 1 2 mpbir x x = y