Theorem ct2 58

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

Hypotheses

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

Assertion

Ref	Expression
ct2	⊢ (T, R)⊧(T, S)

Proof of Theorem ct2

Step	Hyp	Ref	Expression
1		ct1.2	. . 3 ⊢ T:∗
2		ct1.1	. . . 4 ⊢ R⊧S
3	2	ax-cb1 29	. . 3 ⊢ R:∗
4	1, 3	simpl 22	. 2 ⊢ (T, R)⊧T
5	2, 1	adantl 56	. 2 ⊢ (T, R)⊧S
6	4, 5	jca 18	1 ⊢ (T, R)⊧(T, S)

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  ax-wctl 31  ax-wctr 32

This theorem is referenced by: (None)