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Mirrors > Home > ILE Home > Th. List > pm5.1im | Unicode version |
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 . (Contributed by Wolf Lammen, 12-May-2013.) |
Ref | Expression |
---|---|
pm5.1im |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . 2 | |
2 | ax-1 6 | . 2 | |
3 | 1, 2 | impbid21d 127 | 1 |
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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