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Metamath Proof Explorer

Theorem eelT0

Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses eelT0.1 ⊢ ( ⊤ → 𝜑 )
eelT0.2 ⊢ 𝜓
eelT0.3 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion eelT0 𝜒

Proof

Step Hyp Ref Expression
1 eelT0.1 ⊢ ( ⊤ → 𝜑 )
2 eelT0.2 ⊢ 𝜓
3 eelT0.3 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
4 1 3 sylan ⊢ ( ( ⊤ ∧ 𝜓 ) → 𝜒 )
5 2 4 mpan2 ⊢ ( ⊤ → 𝜒 )
6 5 mptru ⊢ 𝜒