Theorem neor 1636

Description: Logical OR with an equality.

Assertion

Ref	Expression
neor	|- ((A = B \/ ps) <-> (A =/= B -> ps))

Proof of Theorem neor

Step	Hyp	Ref	Expression
1		df-or 224	. 2 |- ((A = B \/ ps) <-> (-. A = B -> ps))
2		df-ne 1585	. . 3 |- (A =/= B <-> -. A = B)
3	2	imbi1i 186	. 2 |- ((A =/= B -> ps) <-> (-. A = B -> ps))
4	1, 3	bitr4 176	1 |- ((A = B \/ ps) <-> (A =/= B -> ps))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222   = wceq 955   =/= wne 1583

This theorem is referenced by:  primet 6152  elfzp1 6455  infxpidmlem12 7523  h1datom 9461  elat2 10223

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-ne 1585

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