Metamath Proof Explorer

Theorem nfcvf2

Description: If x and y are distinct, then y is not free in x . Usage of this theorem is discouraged because it depends on ax-13 . See nfcv for a version that replaces the distinctor with a disjoint variable condition, requiring fewer axioms. (Contributed by Mario Carneiro, 5-Dec-2016) (New usage is discouraged.)

Ref Expression
Assertion nfcvf2 ( ¬ ∀ 𝑥 𝑥 = 𝑦 𝑦 𝑥 )


Step Hyp Ref Expression
1 nfcvf ( ¬ ∀ 𝑦 𝑦 = 𝑥 𝑦 𝑥 )
2 1 naecoms ( ¬ ∀ 𝑥 𝑥 = 𝑦 𝑦 𝑥 )