Metamath Proof Explorer


Theorem 3ornot23VD

Description: Virtual deduction proof of 3ornot23 . The following user's proof is completed by invoking mmj2's unify command and using mmj2's StepSelector to pick all remaining steps of the Metamath proof.

1::
|- (. ( -. ph /\ -. ps ) ->. ( -. ph /\ -. ps ) ).
2:: |- (. ( -. ph /\ -. ps ) ,. ( ch \/ ph \/ ps ) ->. ( ch \/ ph \/ ps ) ).
3:1,?: e1a |- (. ( -. ph /\ -. ps ) ->. -. ph ).
4:1,?: e1a |- (. ( -. ph /\ -. ps ) ->. -. ps ).
5:3,4,?: e11 |- (. ( -. ph /\ -. ps ) ->. -. ( ph \/ ps ) ).
6:2,?: e2 |- (. ( -. ph /\ -. ps ) ,. ( ch \/ ph \/ ps ) ->. ( ch \/ ( ph \/ ps ) ) ).
7:5,6,?: e12 |- (. ( -. ph /\ -. ps ) ,. ( ch \/ ph \/ ps ) ->. ch ).
8:7: |- (. ( -. ph /\ -. ps ) ->. ( ( ch \/ ph \/ ps ) -> ch ) ).
qed:8: |- ( ( -. ph /\ -. ps ) -> ( ( ch \/ ph \/ ps ) -> ch ) )
(Contributed by Alan Sare, 31-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion 3ornot23VD ¬ φ ¬ ψ χ φ ψ χ

Proof

Step Hyp Ref Expression
1 idn1 ¬ φ ¬ ψ ¬ φ ¬ ψ
2 simpl ¬ φ ¬ ψ ¬ φ
3 1 2 e1a ¬ φ ¬ ψ ¬ φ
4 simpr ¬ φ ¬ ψ ¬ ψ
5 1 4 e1a ¬ φ ¬ ψ ¬ ψ
6 ioran ¬ φ ψ ¬ φ ¬ ψ
7 6 simplbi2 ¬ φ ¬ ψ ¬ φ ψ
8 3 5 7 e11 ¬ φ ¬ ψ ¬ φ ψ
9 idn2 ¬ φ ¬ ψ , χ φ ψ χ φ ψ
10 3orass χ φ ψ χ φ ψ
11 10 biimpi χ φ ψ χ φ ψ
12 9 11 e2 ¬ φ ¬ ψ , χ φ ψ χ φ ψ
13 orel2 ¬ φ ψ χ φ ψ χ
14 8 12 13 e12 ¬ φ ¬ ψ , χ φ ψ χ
15 14 in2 ¬ φ ¬ ψ χ φ ψ χ
16 15 in1 ¬ φ ¬ ψ χ φ ψ χ