Description: A virtual deduction elimination rule (see syl10 ). (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
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Hypotheses | e23.1 | |- (. ph ,. ps ->. ch ). |
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e23.2 | |- (. ph ,. ps ,. th ->. ta ). |
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e23.3 | |- ( ch -> ( ta -> et ) ) |
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Assertion | e23 | |- (. ph ,. ps ,. th ->. et ). |
Step | Hyp | Ref | Expression |
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1 | e23.1 | |- (. ph ,. ps ->. ch ). |
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2 | e23.2 | |- (. ph ,. ps ,. th ->. ta ). |
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3 | e23.3 | |- ( ch -> ( ta -> et ) ) |
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4 | 1 | vd23 | |- (. ph ,. ps ,. th ->. ch ). |
5 | 4 2 3 | e33 | |- (. ph ,. ps ,. th ->. et ). |