Theorem ct1 57

Description: Introduce a right conjunct. (Contributed by Mario Carneiro, 30-Sep-2023.)

Hypotheses

Ref	Expression
ct1.1	⊢ R⊧S
ct1.2	⊢ T:∗

Assertion

Ref	Expression
ct1	⊢ (R, T)⊧(S, T)

Proof of Theorem ct1

Step	Hyp	Ref	Expression
1		ct1.1	. . 3 ⊢ R⊧S
2		ct1.2	. . 3 ⊢ T:∗
3	1, 2	adantr 55	. 2 ⊢ (R, T)⊧S
4	1	ax-cb1 29	. . 3 ⊢ R:∗
5	4, 2	simpr 23	. 2 ⊢ (R, T)⊧T
6	3, 5	jca 18	1 ⊢ (R, T)⊧(S, T)

Syntax hints:  ∗hb 3  kct 10  ⊧wffMMJ2 11  wffMMJ2t 12

This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-cb1 29

This theorem is referenced by:  an32s  60  anassrs  62