Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 17-Apr-2012) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | e323.1 | |- (. ph ,. ps ,. ch ->. th ). |
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e323.2 | |- (. ph ,. ps ->. ta ). |
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e323.3 | |- (. ph ,. ps ,. ch ->. et ). |
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e323.4 | |- ( th -> ( ta -> ( et -> ze ) ) ) |
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Assertion | e323 | |- (. ph ,. ps ,. ch ->. ze ). |
Step | Hyp | Ref | Expression |
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1 | e323.1 | |- (. ph ,. ps ,. ch ->. th ). |
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2 | e323.2 | |- (. ph ,. ps ->. ta ). |
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3 | e323.3 | |- (. ph ,. ps ,. ch ->. et ). |
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4 | e323.4 | |- ( th -> ( ta -> ( et -> ze ) ) ) |
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5 | 1 | dfvd3i | |- ( ph -> ( ps -> ( ch -> th ) ) ) |
6 | 2 | dfvd2i | |- ( ph -> ( ps -> ta ) ) |
7 | 3 | dfvd3i | |- ( ph -> ( ps -> ( ch -> et ) ) ) |
8 | 5 6 7 4 | ee323 | |- ( ph -> ( ps -> ( ch -> ze ) ) ) |
9 | 8 | dfvd3ir | |- (. ph ,. ps ,. ch ->. ze ). |