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Metamath Proof Explorer

Theorem mp2b

Description: A double modus ponens inference. (Contributed by Mario Carneiro, 24-Jan-2013)

Ref Expression
Hypotheses mp2b.1 ⊢ φ
mp2b.2 ⊢ φ → ψ
mp2b.3 ⊢ ψ → χ
Assertion mp2b ⊢ χ

Proof

Step Hyp Ref Expression
1 mp2b.1 ⊢ φ
2 mp2b.2 ⊢ φ → ψ
3 mp2b.3 ⊢ ψ → χ
4 1 2 ax-mp ⊢ ψ
5 4 3 ax-mp ⊢ χ