Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | e123.1 | |- (. ph ->. ps ). |
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e123.2 | |- (. ph ,. ch ->. th ). |
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e123.3 | |- (. ph ,. ch ,. ta ->. et ). |
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e123.4 | |- ( ps -> ( th -> ( et -> ze ) ) ) |
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Assertion | e123 | |- (. ph ,. ch ,. ta ->. ze ). |
Step | Hyp | Ref | Expression |
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1 | e123.1 | |- (. ph ->. ps ). |
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2 | e123.2 | |- (. ph ,. ch ->. th ). |
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3 | e123.3 | |- (. ph ,. ch ,. ta ->. et ). |
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4 | e123.4 | |- ( ps -> ( th -> ( et -> ze ) ) ) |
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5 | 1 | vd13 | |- (. ph ,. ch ,. ta ->. ps ). |
6 | 2 | vd23 | |- (. ph ,. ch ,. ta ->. th ). |
7 | 5 6 3 4 | e333 | |- (. ph ,. ch ,. ta ->. ze ). |