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Theorem pm5.1im 229
Description: Two propositions are equivalent if they are both true. Closed form of 2th 230. Equivalent to a bi1 178-like version of the xor-connective. This theorem stays true, no matter how you permute its operands. This is evident from its sharper version  ( ph  <->  ( ps  <->  (
ph 
<->  ps ) ) ). (Contributed by Wolf Lammen, 12-May-2013.)
Assertion
Ref Expression
pm5.1im  |-  ( ph  ->  ( ps  ->  ( ph 
<->  ps ) ) )

Proof of Theorem pm5.1im
StepHypRef Expression
1 ax-1 5 . 2  |-  ( ps 
->  ( ph  ->  ps ) )
2 ax-1 5 . 2  |-  ( ph  ->  ( ps  ->  ph )
)
31, 2impbid21d 182 1  |-  ( ph  ->  ( ps  ->  ( ph 
<->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
This theorem is referenced by:  2thd  231  pm5.501  330
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177
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