Theorem mp2ani 523

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mp2ani.1	⊢ ψ
mp2ani.2	⊢ χ
mp2ani.3	⊢ (φ → ((ψ ∧ χ) → θ))

Assertion

Ref	Expression
mp2ani	⊢ (φ → θ)

Proof of Theorem mp2ani

Step	Hyp	Ref	Expression
1		mp2ani.2	. 2 ⊢ χ
2		mp2ani.1	. . 3 ⊢ ψ
3		mp2ani.3	. . 3 ⊢ (φ → ((ψ ∧ χ) → θ))
4	2, 3	mpani 521	. 2 ⊢ (φ → (χ → θ))
5	1, 4	mpi 44	1 ⊢ (φ → θ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  th3q 3253  dfom3 3477  aceq5lem4 3561  cflem 3700  pjcomp 5565  pjoi0 5592  sto1 5677  stji1 5683  stcltr1 5707

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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