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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 172. Equivalent to a bi1 116-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 5 | . 2 | |
2 | ax-1 5 | . 2 | |
3 | 1, 2 | impbid21d 126 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: 2thd 173 pm5.501 242 dcextest 4386 snexxph 6638 |
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