Theorem jctild 316

Description: Deduction conjoining a theorem to left of consequent in an implication. (Contributed by NM, 21-Apr-2005.)

Hypotheses

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

Assertion

Ref	Expression
jctild	⊢ (𝜑 → (𝜓 → (𝜃 ∧ 𝜒)))

Proof of Theorem jctild

Step	Hyp	Ref	Expression
1		jctild.2	. . 3 ⊢ (𝜑 → 𝜃)
2	1	a1d 22	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
3		jctild.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
4	2, 3	jcad 307	1 ⊢ (𝜑 → (𝜓 → (𝜃 ∧ 𝜒)))

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108

This theorem is referenced by:  anc2li  329  syl6an  1445  poxp  6299  ssenen  6921  aptiprleml  7723  zmulcl  9396  rexuz3  11172  cau3lem  11296  gcdzeq  12214  isprm3  12311  epttop  14410  lmtopcnp  14570  txcnp  14591