Description: Obsolete version of opabresex2 as of 13-Dec-2024. (Contributed by Alexander van der Vekens, 1-Nov-2017) (Revised by AV, 30-Dec-2020) (Proof shortened by AV, 15-Jan-2021) (New usage is discouraged.) (Proof modification is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | wlkResOLD.1 | |- ( f ( W ` G ) p -> f ( Walks ` G ) p ) |
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Assertion | wlkResOLD | |- { <. f , p >. | ( f ( W ` G ) p /\ ph ) } e. _V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wlkResOLD.1 | |- ( f ( W ` G ) p -> f ( Walks ` G ) p ) |
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2 | 1 | gen2 | |- A. f A. p ( f ( W ` G ) p -> f ( Walks ` G ) p ) |
3 | wksv | |- { <. f , p >. | f ( Walks ` G ) p } e. _V |
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4 | opabbrex | |- ( ( A. f A. p ( f ( W ` G ) p -> f ( Walks ` G ) p ) /\ { <. f , p >. | f ( Walks ` G ) p } e. _V ) -> { <. f , p >. | ( f ( W ` G ) p /\ ph ) } e. _V ) |
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5 | 2 3 4 | mp2an | |- { <. f , p >. | ( f ( W ` G ) p /\ ph ) } e. _V |