Theorem imsubr-P3.28b 269

Description: Implication Substitution (right). †

Hypothesis

Ref	Expression
imsubr-P3.28b.1	⊢ (𝛾 → (𝜑 → 𝜓))

Assertion

Ref	Expression
imsubr-P3.28b	⊢ (𝛾 → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Proof of Theorem imsubr-P3.28b

Step	Hyp	Ref	Expression
1		rcp-NDASM2of2 194	. . 3 ⊢ ((𝛾 ∧ (𝜒 → 𝜑)) → (𝜒 → 𝜑))
2		imsubr-P3.28b.1	. . . 4 ⊢ (𝛾 → (𝜑 → 𝜓))
3	2	rcp-NDIMP1add1 208	. . 3 ⊢ ((𝛾 ∧ (𝜒 → 𝜑)) → (𝜑 → 𝜓))
4	1, 3	syl-P3.24 259	. 2 ⊢ ((𝛾 ∧ (𝜒 → 𝜑)) → (𝜒 → 𝜓))
5	4	rcp-NDIMI2 224	1 ⊢ (𝛾 → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Syntax hints:   → wff-imp 10   ∧ 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:  imsubr-P3.28b.RC  270  imsubd-P3.28c  271  subimr-P3.40b  327