Theorem alinexa 724

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 207	. . 3 |- ((ph -> -. ps) <-> -. (ph /\ ps))
2	1	bial 695	. 2 |- (A.x(ph -> -. ps) <-> A.x -. (ph /\ ps))
3		alnex 716	. 2 |- (A.x -. (ph /\ ps) <-> -. E.x(ph /\ ps))
4	2, 3	bitr 151	1 |- (A.x(ph -> -. ps) <-> -. E.x(ph /\ ps))

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127   /\ wa 196  A.wal 672  E.wex 678

This theorem is referenced by:  eqs3 830  ralnex 1209  zornlem4 3606  suplem2pr 3956  nnunb 4520

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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