Metamath Proof Explorer


Theorem ee011

Description: e011 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee011.1 ⊢ 𝜑
ee011.2 ⊢ ( 𝜓 → 𝜒 )
ee011.3 ⊢ ( 𝜓 → 𝜃 )
ee011.4 ⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion ee011 ( 𝜓 → 𝜏 )

Proof

Step Hyp Ref Expression
1 ee011.1 ⊢ 𝜑
2 ee011.2 ⊢ ( 𝜓 → 𝜒 )
3 ee011.3 ⊢ ( 𝜓 → 𝜃 )
4 ee011.4 ⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5 1 a1i ⊢ ( 𝜓 → 𝜑 )
6 5 2 3 4 syl3c ⊢ ( 𝜓 → 𝜏 )