Theorem imsubl-P1.7b 54

Description: Implication Substitution (left).

The other related rule is imsubr-P1.7a 51.

Assertion

Ref	Expression
imsubl-P1.7b	⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))

Proof of Theorem imsubl-P1.7b

Step	Hyp	Ref	Expression
1		imsubr-P1.7a 51	. 2 ⊢ ((𝜓 → 𝜒) → ((𝜑 → 𝜓) → (𝜑 → 𝜒)))
2	1	imcomm-P1.6.SH 49	1 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒)))

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:  imsubl-P1.7b.SH  55  imsubl-P1.7b.AC.SH  56  sylt-P1.9  61