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Metamath Proof Explorer

Theorem eel3132

Description: syl2an with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016)

Ref Expression
Hypotheses eel3132.1 ⊢ φ ∧ ψ → χ
eel3132.2 ⊢ θ ∧ ψ → τ
eel3132.3 ⊢ χ ∧ τ → η
Assertion eel3132 ⊢ φ ∧ θ ∧ ψ → η

Proof

Step Hyp Ref Expression
1 eel3132.1 ⊢ φ ∧ ψ → χ
2 eel3132.2 ⊢ θ ∧ ψ → τ
3 eel3132.3 ⊢ χ ∧ τ → η
4 1 2 3 syl2an ⊢ φ ∧ ψ ∧ θ ∧ ψ → η
5 4 3impdir ⊢ φ ∧ θ ∧ ψ → η