Theorem alinexa 1040

Description: A transformation of quantifiers and logical connectives.

Assertion

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

Proof of Theorem alinexa

Step	Hyp	Ref	Expression
1		imnan 242	. . 3 |- ((ph -> -. ps) <-> -. (ph /\ ps))
2	1	albii 997	. 2 |- (A.x(ph -> -. ps) <-> A.x -. (ph /\ ps))
3		alnex 1031	. 2 |- (A.x -. (ph /\ ps) <-> -. E.x(ph /\ ps))
4	2, 3	bitr 173	1 |- (A.x(ph -> -. ps) <-> -. E.x(ph /\ ps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   /\ wa 223  A.wal 952  E.wex 978

This theorem is referenced by:  equs3 1147  ralnex 1650  ac6n 4737  suplem2pr 5142  nnunb 6025

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-4 971  ax-5o 973

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979

Copyright terms: Public domain