Theorem imnang 1769

Description: Quantified implication in terms of quantified negation of conjunction. (Contributed by BJ, 16-Jul-2021.)

Assertion

Ref	Expression
imnang	|- ( A. x ( ph -> -. ps ) <-> A. x -. ( ph /\ ps ) )

Proof of Theorem imnang

Step	Hyp	Ref	Expression
1		imnan 438	. 2 |- ( ( ph -> -. ps ) <-> -. ( ph /\ ps ) )
2	1	albii 1747	1 |- ( A. x ( ph -> -. ps ) <-> A. x -. ( ph /\ ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   /\ wa 384   A.wal 1481

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

This theorem is referenced by:  alinexa  1770  raln  2991  n0el  3940  ballotlem2  30550