Metamath Proof Explorer


Theorem ee120

Description: Virtual deduction rule e120 without virtual deduction symbols. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee120.1 φ ψ
ee120.2 φ χ θ
ee120.3 τ
ee120.4 ψ θ τ η
Assertion ee120 φ χ η

Proof

Step Hyp Ref Expression
1 ee120.1 φ ψ
2 ee120.2 φ χ θ
3 ee120.3 τ
4 ee120.4 ψ θ τ η
5 1 a1d φ χ ψ
6 3 a1i χ τ
7 6 a1i φ χ τ
8 5 2 7 4 ee222 φ χ η