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Mirrors > Home > MPE Home > Th. List > Mathboxes > pm2.43bgbi | Structured version Visualization version Unicode version |
Description: Logical equivalence of a 2-left-nested implication and a 1-left-nested
implicated
when two antecedents of the former implication are identical.
(Contributed by Alan Sare, 18-Mar-2012.)
(Proof modification is discouraged.) (New usage is discouraged.)
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. The
completed Virtual
Deduction Proof (not shown) was minimized. The minimized proof is
shown.
|
Ref | Expression |
---|---|
pm2.43bgbi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mercolem6 1667 | . 2 | |
2 | ax-1 6 | . 2 | |
3 | 1, 2 | impbii 199 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-tru 1486 df-fal 1489 |
This theorem is referenced by: (None) |
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