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Theorem pm5.1im 162
Description: Two propositions are equivalent if they are both true. Closed form of 2th 163. Equivalent to a bi1 111-like version of the xor-connective. This theorem stays true, no matter how you permute its operands. This is evident from its sharper version . (Contributed by Wolf Lammen, 12-May-2013.)
Ref Expression

Proof of Theorem pm5.1im
StepHypRef Expression
1 ax-1 5 . 2
2 ax-1 5 . 2
31, 2impbid21d 119 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  2thd  164  pm5.501  233
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