Theorem eelT0 44800

Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
eelT0.1	⊢ (⊤ → 𝜑)
eelT0.2	⊢ 𝜓
eelT0.3	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
eelT0	⊢ 𝜒

Proof of Theorem eelT0

Step	Hyp	Ref	Expression
1		eelT0.2	. . 3 ⊢ 𝜓
2		eelT0.1	. . . 4 ⊢ (⊤ → 𝜑)
3		eelT0.3	. . . 4 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
4	2, 3	sylan 580	. . 3 ⊢ ((⊤ ∧ 𝜓) → 𝜒)
5	1, 4	mpan2 691	. 2 ⊢ (⊤ → 𝜒)
6	5	mptru 1546	1 ⊢ 𝜒

Syntax hints:   → wi 4   ∧ wa 395  ⊤wtru 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542

This theorem is referenced by: (None)