Theorem jctil 523

Description: Inference conjoining a theorem to left of consequent in an implication. (Contributed by NM, 31-Dec-1993.)

Hypotheses

Ref	Expression
jctil.1	⊢ (φ → ψ)
jctil.2	⊢ χ

Assertion

Ref	Expression
jctil	⊢ (φ → (χ ∧ ψ))

Proof of Theorem jctil

Step	Hyp	Ref	Expression
1		jctil.2	. . 3 ⊢ χ
2	1	a1i 10	. 2 ⊢ (φ → χ)
3		jctil.1	. 2 ⊢ (φ → ψ)
4	2, 3	jca 518	1 ⊢ (φ → (χ ∧ ψ))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  jctl  525  nic-ax  1438  nic-axALT  1439  unidif  3924  iunxdif2  4015  sbthlem1  6204