Theorem subandl2-P4 552

Description: Alternate Form of subandl-P3.42a 339. †

Hypotheses

Ref	Expression
subandl2-P4.1	⊢ (𝛾 → (𝜑 ∧ 𝜒))
subandl2-P4.2	⊢ (𝛾 → (𝜑 ↔ 𝜓))

Assertion

Ref	Expression
subandl2-P4	⊢ (𝛾 → (𝜓 ∧ 𝜒))

Proof of Theorem subandl2-P4

Step	Hyp	Ref	Expression
1		subandl2-P4.1	. 2 ⊢ (𝛾 → (𝜑 ∧ 𝜒))
2		subandl2-P4.2	. . . 4 ⊢ (𝛾 → (𝜑 ↔ 𝜓))
3	2	subandl-P3.42a 339	. . 3 ⊢ (𝛾 → ((𝜑 ∧ 𝜒) ↔ (𝜓 ∧ 𝜒)))
4	3	ndbief-P3.14 179	. 2 ⊢ (𝛾 → ((𝜑 ∧ 𝜒) → (𝜓 ∧ 𝜒)))
5	1, 4	ndime-P3.6 171	1 ⊢ (𝛾 → (𝜓 ∧ 𝜒))

Syntax hints:   → wff-imp 10   ↔ wff-bi 104   ∧ wff-and 132

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133

This theorem is referenced by:  subandl2-P4.RC  553