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Theorem e333 28919
 Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e333.1
e333.2
e333.3
e333.4
Assertion
Ref Expression
e333

Proof of Theorem e333
StepHypRef Expression
1 e333.3 . . . . . . 7
21dfvd3i 28758 . . . . . 6
323imp 1148 . . . . 5
4 e333.1 . . . . . . . . 9
54dfvd3i 28758 . . . . . . . 8
653imp 1148 . . . . . . 7
7 e333.2 . . . . . . . . 9
87dfvd3i 28758 . . . . . . . 8
983imp 1148 . . . . . . 7
10 e333.4 . . . . . . 7
116, 9, 10syl2im 37 . . . . . 6
1211pm2.43i 46 . . . . 5
133, 12syl5com 29 . . . 4
1413pm2.43i 46 . . 3
15143exp 1153 . 2
1615dfvd3ir 28759 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 937  wvd3 28753 This theorem is referenced by:  e33  28920  e123  28948 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-vd3 28756
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