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Metamath Proof Explorer

Theorem ee100

Description: e100 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ee100.1 ⊢ ( 𝜑 → 𝜓 )
ee100.2 ⊢ 𝜒
ee100.3 ⊢ 𝜃
ee100.4 ⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
Assertion ee100 ( 𝜑 → 𝜏 )

Proof

Step Hyp Ref Expression
1 ee100.1 ⊢ ( 𝜑 → 𝜓 )
2 ee100.2 ⊢ 𝜒
3 ee100.3 ⊢ 𝜃
4 ee100.4 ⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
5 2 a1i ⊢ ( 𝜑 → 𝜒 )
6 3 a1i ⊢ ( 𝜑 → 𝜃 )
7 1 5 6 4 syl3c ⊢ ( 𝜑 → 𝜏 )