Theorem imsubr-P1.7a 51

Description: Implication Substitution (right).

The other related rule is imsubl-P1.7b 54.

Assertion

Ref	Expression
imsubr-P1.7a	⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Proof of Theorem imsubr-P1.7a

Step	Hyp	Ref	Expression
1		ax-L1 11	. 2 ⊢ ((𝜑 → 𝜓) → (𝜒 → (𝜑 → 𝜓)))
2	1	axL2.AC.SH 46	1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜑) → (𝜒 → 𝜓)))

Syntax hints:   → wff-imp 10

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

This theorem is referenced by:  imsubr-P1.7a.SH  52  imsubr-P1.7a.AC.SH  53  imsubl-P1.7b  54