Theorem mp2and 526

Description: A deduction based on modus ponens.

Hypotheses

Ref	Expression
mp2and.1	⊢ (φ → ψ)
mp2and.2	⊢ (φ → χ)
mp2and.3	⊢ (φ → ((ψ ∧ χ) → θ))

Assertion

Ref	Expression
mp2and	⊢ (φ → θ)

Proof of Theorem mp2and

Step	Hyp	Ref	Expression
1		mp2and.2	. 2 ⊢ (φ → χ)
2		mp2and.1	. . 3 ⊢ (φ → ψ)
3		mp2and.3	. . 3 ⊢ (φ → ((ψ ∧ χ) → θ))
4	2, 3	mpand 524	. 2 ⊢ (φ → (χ → θ))
5	1, 4	mpd 46	1 ⊢ (φ → θ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  euuni 1954  tfindsg2 2403  zltp1let 4597  infxpidmlem12 4944  stadd 5687  stadd3 5689  atcvatlem 5770

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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