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Theorem pm5.1im 172
Description: Two propositions are equivalent if they are both true. Closed form of 2th 173. Equivalent to a bi1 117-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 6 . 2  |-  ( ps 
->  ( ph  ->  ps ) )
2 ax-1 6 . 2  |-  ( ph  ->  ( ps  ->  ph )
)
31, 2impbid21d 127 1  |-  ( ph  ->  ( ps  ->  ( ph 
<->  ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  2thd  174  pm5.501  243  dcextest  4463  snexxph  6804
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