Theorem mp2b 9

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

Hypotheses

Ref	Expression
mp2b.1	⊢ φ
mp2b.2	⊢ (φ → ψ)
mp2b.3	⊢ (ψ → χ)

Assertion

Ref	Expression
mp2b	⊢ χ

Proof of Theorem mp2b

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

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5

This theorem is referenced by:  equid  1676  eqvinc  2967  nfunv  5139  funres11  5165  fundmen  6044  xpsnen  6050  xpassen  6058  ncssfin  6152  ce0addcnnul  6180