Theorem alinexa 1044

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 1001	. 2 |- (A.x(ph -> -. ps) <-> A.x -. (ph /\ ps))
3		alnex 1035	. 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 956  E.wex 982

This theorem is referenced by:  equs3 1151  ralnex 1656  ac6n 4767  suplem2pr 5174  nnunb 6072

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-4 975  ax-5o 977

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983

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