Metamath Proof Explorer

Theorem nfim

Description: If x is not free in ph and ps , then it is not free in ( ph -> ps ) . Inference associated with nfimt . (Contributed by Mario Carneiro, 11-Aug-2016) (Proof shortened by Wolf Lammen, 2-Jan-2018) df-nf changed. (Revised by Wolf Lammen, 17-Sep-2021)

Ref Expression
Hypotheses nfim.1 x φ
nfim.2 x ψ
Assertion nfim x φ ψ


Step Hyp Ref Expression
1 nfim.1 x φ
2 nfim.2 x ψ
3 nfimt x φ x ψ x φ ψ
4 1 2 3 mp2an x φ ψ