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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
StepHypRef Expression
1 ct1.2 . . 3 |- T:*
2 ct1.1 . . . 4 |- R |= S
32ax-cb1 29 . . 3 |- R:*
41, 3simpl 22 . 2 |- (T, R) |= T
52, 1adantl 56 . 2 |- (T, R) |= S
64, 5jca 18 1 |- (T, R) |= (T, S)
Colors of variables: type var term
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)
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