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Metamath Proof Explorer

Theorem eelTT

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

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

Proof

Step Hyp Ref Expression
1 eelTT.1 ⊢ ( ⊤ → 𝜑 )
2 eelTT.2 ⊢ ( ⊤ → 𝜓 )
3 eelTT.3 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
4 truan ⊢ ( ( ⊤ ∧ 𝜓 ) ↔ 𝜓 )
5 1 3 sylan ⊢ ( ( ⊤ ∧ 𝜓 ) → 𝜒 )
6 4 5 sylbir ⊢ ( 𝜓 → 𝜒 )
7 2 6 syl ⊢ ( ⊤ → 𝜒 )
8 7 mptru ⊢ 𝜒