Theorem nfimt2 1822

Description: Closed form of nfim 1825 and uncurried (imported) form of nfimt 1821. (Contributed by BJ, 20-Oct-2021.)

Assertion

Ref	Expression
nfimt2	|- ( ( F/ x ph /\ F/ x ps ) -> F/ x ( ph -> ps ) )

Proof of Theorem nfimt2

Step	Hyp	Ref	Expression
1		nfimt 1821	. 2 |- ( F/ x ph -> ( F/ x ps -> F/ x ( ph -> ps ) ) )
2	1	imp 445	1 |- ( ( F/ x ph /\ F/ x ps ) -> F/ x ( ph -> ps ) )

Syntax hints:   -> wi 4   /\ wa 384   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  nfimd  1823  nfim  1825