Metamath Proof Explorer


Theorem eel2131

Description: syl2an with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016)

Ref Expression
Hypotheses eel2131.1 ( ( 𝜑𝜓 ) → 𝜒 )
eel2131.2 ( ( 𝜑𝜃 ) → 𝜏 )
eel2131.3 ( ( 𝜒𝜏 ) → 𝜂 )
Assertion eel2131 ( ( 𝜑𝜓𝜃 ) → 𝜂 )

Proof

Step Hyp Ref Expression
1 eel2131.1 ( ( 𝜑𝜓 ) → 𝜒 )
2 eel2131.2 ( ( 𝜑𝜃 ) → 𝜏 )
3 eel2131.3 ( ( 𝜒𝜏 ) → 𝜂 )
4 1 2 3 syl2an ( ( ( 𝜑𝜓 ) ∧ ( 𝜑𝜃 ) ) → 𝜂 )
5 4 3impdi ( ( 𝜑𝜓𝜃 ) → 𝜂 )