Metamath Proof Explorer

Theorem drnf2

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Usage of this theorem is discouraged because it depends on ax-13 . Usage of nfbidv is preferred, which requires fewer axioms. (Contributed by Mario Carneiro, 4-Oct-2016) (Proof shortened by Wolf Lammen, 5-May-2018) (New usage is discouraged.)

Ref Expression
Hypothesis dral1.1 x x = y φ ψ
Assertion drnf2 x x = y z φ z ψ


Step Hyp Ref Expression
1 dral1.1 x x = y φ ψ
2 nfae z x x = y
3 2 1 nfbidf x x = y z φ z ψ