Description: Part of proof of Lemma E in Crawley p. 113. Lemma leading to cdleme3fa and cdleme3 . (Contributed by NM, 6-Jun-2012)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | cdleme1.l | |- .<_ = ( le ` K ) |
|
| cdleme1.j | |- .\/ = ( join ` K ) |
||
| cdleme1.m | |- ./\ = ( meet ` K ) |
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| cdleme1.a | |- A = ( Atoms ` K ) |
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| cdleme1.h | |- H = ( LHyp ` K ) |
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| cdleme1.u | |- U = ( ( P .\/ Q ) ./\ W ) |
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| cdleme1.f | |- F = ( ( R .\/ U ) ./\ ( Q .\/ ( ( P .\/ R ) ./\ W ) ) ) |
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| cdleme3.3 | |- V = ( ( P .\/ R ) ./\ W ) |
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| Assertion | cdleme3d | |- F = ( ( R .\/ U ) ./\ ( Q .\/ V ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cdleme1.l | |- .<_ = ( le ` K ) |
|
| 2 | cdleme1.j | |- .\/ = ( join ` K ) |
|
| 3 | cdleme1.m | |- ./\ = ( meet ` K ) |
|
| 4 | cdleme1.a | |- A = ( Atoms ` K ) |
|
| 5 | cdleme1.h | |- H = ( LHyp ` K ) |
|
| 6 | cdleme1.u | |- U = ( ( P .\/ Q ) ./\ W ) |
|
| 7 | cdleme1.f | |- F = ( ( R .\/ U ) ./\ ( Q .\/ ( ( P .\/ R ) ./\ W ) ) ) |
|
| 8 | cdleme3.3 | |- V = ( ( P .\/ R ) ./\ W ) |
|
| 9 | 8 | oveq2i | |- ( Q .\/ V ) = ( Q .\/ ( ( P .\/ R ) ./\ W ) ) |
| 10 | 9 | oveq2i | |- ( ( R .\/ U ) ./\ ( Q .\/ V ) ) = ( ( R .\/ U ) ./\ ( Q .\/ ( ( P .\/ R ) ./\ W ) ) ) |
| 11 | 7 10 | eqtr4i | |- F = ( ( R .\/ U ) ./\ ( Q .\/ V ) ) |