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Metamath Proof Explorer

Theorem syl2an2

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

Ref Expression
Hypotheses syl2an2.1 ⊢ φ → ψ
syl2an2.2 ⊢ χ ∧ φ → θ
syl2an2.3 ⊢ ψ ∧ θ → τ
Assertion syl2an2 ⊢ χ ∧ φ → τ

Proof

Step Hyp Ref Expression
1 syl2an2.1 ⊢ φ → ψ
2 syl2an2.2 ⊢ χ ∧ φ → θ
3 syl2an2.3 ⊢ ψ ∧ θ → τ
4 1 adantl ⊢ χ ∧ φ → ψ
5 4 2 3 syl2anc ⊢ χ ∧ φ → τ