Theorem alinexa 1083

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 249	. . 3 |- ((ph -> -. ps) <-> -. (ph /\ ps))
2	1	albii 1040	. 2 |- (A.x(ph -> -. ps) <-> A.x -. (ph /\ ps))
3		alnex 1074	. 2 |- (A.x -. (ph /\ ps) <-> -. E.x(ph /\ ps))
4	2, 3	bitri 180	1 |- (A.x(ph -> -. ps) <-> -. E.x(ph /\ ps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 153   /\ wa 230  A.wal 995  E.wex 1021

This theorem is referenced by:  equs3 1191  ralnex 1700  ac6n 4819  suplem2pr 5227  nnunb 6152

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1004  ax-4 1014  ax-5o 1016

This theorem depends on definitions:  df-bi 154  df-an 232  df-ex 1022

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